Mathematics · Textbook solutions

Statistics

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 30 questions

13.2 Mean of Grouped Data

12 q

Solved Examples

Worked · 3

13.1 Eg.1 $x_i$
13.1 Eg.2 $The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by all the three methods discussed in this section. Percentage of female teachers 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75 75 - 85 Number of States/U.T. 61174421 Source : Seventh All India School Education Survey conducted by NCERT$
13.1 Eg.3 $The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify? Number of wickets 20 - 60 60 - 100 100 - 150 150 - 250 250 - 350 350 - 450 Number of bowlers 75161223$

Marks obtained $x_i$	10	20	36	40	50	56	60	70	72	80	88	92	95
Number of students $f_i$	1	1	3	4	3	2	4	4	1	1	2	3	1

Percentage of female teachers	15 - 25	25 - 35	35 - 45	45 - 55	55 - 65	65 - 75	75 - 85
Number of States/U.T.	6	11	7	4	4	2	1

Number of wickets	20 - 60	60 - 100	100 - 150	150 - 250	250 - 350	350 - 450
Number of bowlers	7	5	16	12	2	3

Exercise 13.1

Practice · 9

Ex 13.1 Q1 $A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. Number of plants 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12 12 - 14 Number of houses 1215623 Which method did you use for finding the mean, and why?$
Ex 13.1 Q2 $Consider the following distribution of daily wages of 50 workers of a factory. Daily wages (in ₹) 500 - 520 520 - 540 540 - 560 560 - 580 580 - 600 Number of workers 12148610 Find the mean daily wages of the workers of the factory by using an appropriate method.$
Ex 13.1 Q3 $f$
Ex 13.1 Q4 $Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method. Number of heartbeats per minute 65 - 68 68 - 71 71 - 74 74 - 77 77 - 80 80 - 83 83 - 86 Number of women 2438742$
Ex 13.1 Q5 $In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Number of mangoes 50 - 52 53 - 55 56 - 58 59 - 61 62 - 64 Number of boxes 1511013511525 Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?$
Ex 13.1 Q6 $The table below shows the daily expenditure on food of 25 households in a locality. Daily expenditure (in ₹) 100 - 150 150 - 200 200 - 250 250 - 300 300 - 350 Number of households 451222 Find the mean daily expenditure on food by a suitable method.$
Ex 13.1 Q7 $To find out the concentration of SO₂ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below. Find the mean concentration of SO₂ in the air. Concentration of SO₂ (in ppm) Frequency 0.00 - 0.04 4 0.04 - 0.08 9 0.08 - 0.12 9 0.12 - 0.16 2 0.16 - 0.20 4 0.20 - 0.24 2$
Ex 13.1 Q8 $A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. Number of days 0 - 6 6 - 10 10 - 14 14 - 20 20 - 28 28 - 38 38 - 40 Number of students 111074431$
Ex 13.1 Q9 $The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate. Literacy rate (in %) 45 - 55 55 - 65 65 - 75 75 - 85 85 - 95 Number of cities 3101183$

Number of plants	0 - 2	2 - 4	4 - 6	6 - 8	8 - 10	10 - 12	12 - 14
Number of houses	1	2	1	5	6	2	3

Daily wages (in ₹)	500 - 520	520 - 540	540 - 560	560 - 580	580 - 600
Number of workers	12	14	8	6	10

Daily pocket allowance (in ₹)	11 - 13	13 - 15	15 - 17	17 - 19	19 - 21	21 - 23	23 - 25
Number of children	7	6	9	13	$f$	5	4

Number of heartbeats per minute	65 - 68	68 - 71	71 - 74	74 - 77	77 - 80	80 - 83	83 - 86
Number of women	2	4	3	8	7	4	2

Number of mangoes	50 - 52	53 - 55	56 - 58	59 - 61	62 - 64
Number of boxes	15	110	135	115	25

Daily expenditure (in ₹)	100 - 150	150 - 200	200 - 250	250 - 300	300 - 350
Number of households	4	5	12	2	2

Concentration of SO₂ (in ppm)	Frequency
0.00 - 0.04	4
0.04 - 0.08	9
0.08 - 0.12	9
0.12 - 0.16	2
0.16 - 0.20	4
0.20 - 0.24	2

Number of days	0 - 6	6 - 10	10 - 14	14 - 20	20 - 28	28 - 38	38 - 40
Number of students	11	10	7	4	4	3	1

Literacy rate (in %)	45 - 55	55 - 65	65 - 75	75 - 85	85 - 95
Number of cities	3	10	11	8	3

13.3 Mode of Grouped Data

9 q

Solved Examples

Worked · 3

13.2 Eg.4 $The wickets taken by a bowler in 10 cricket matches are as follows: 2 6 4 5 0 2 1 3 2 3 Find the mode of the data.$
13.2 Eg.5 $A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household. Find the mode of this data. Family size 1 - 3 3 - 5 5 - 7 7 - 9 9 - 11 Number of families 78221$
The marks distribution of 30 students in a mathematics examination is given in Table 13.3 of Example 1, reproduced here:
Class interval 10 - 25 25 - 40 40 - 55 55 - 70 70 - 85 85 - 100
Number of students 2 3 7 6 6 6
The mean of this distribution was found in Example 1 to be 62.
13.2 Eg.6 $Find the mode of this data. Also compare and interpret the mode and the mean.$

Family size	1 - 3	3 - 5	5 - 7	7 - 9	9 - 11
Number of families	7	8	2	2	1

Class interval	10 - 25	25 - 40	40 - 55	55 - 70	70 - 85	85 - 100
Number of students	2	3	7	6	6	6

Exercise 13.2

Practice · 6

Ex 13.2 Q1 $The following table shows the ages of the patients admitted in a hospital during a year: Age (in years) 5 - 15 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 Number of patients 6112123145 Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.$
Ex 13.2 Q2 $The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetimes of the components. Lifetimes (in hours) 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 Frequency 103552613829$
Ex 13.2 Q3 $The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure : Expenditure (in ₹) Number of families 1000 - 1500 24 1500 - 2000 40 2000 - 2500 33 2500 - 3000 28 3000 - 3500 30 3500 - 4000 22 4000 - 4500 16 4500 - 5000 7$
Ex 13.2 Q4 $The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures. Number of students per teacher Number of states / U.T. 15 - 20 3 20 - 25 8 25 - 30 9 30 - 35 10 35 - 40 3 40 - 45 0 45 - 50 0 50 - 55 2$
Ex 13.2 Q5 $The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Find the mode of the data. Runs scored Number of batsmen 3000 - 4000 4 4000 - 5000 18 5000 - 6000 9 6000 - 7000 7 7000 - 8000 6 8000 - 9000 3 9000 - 10000 1 10000 - 11000 1$
Ex 13.2 Q6 $A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data : Number of cars 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency 71413122011158$

Age (in years)	5 - 15	15 - 25	25 - 35	35 - 45	45 - 55	55 - 65
Number of patients	6	11	21	23	14	5

Lifetimes (in hours)	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	10	35	52	61	38	29

Expenditure (in ₹)	Number of families
1000 - 1500	24
1500 - 2000	40
2000 - 2500	33
2500 - 3000	28
3000 - 3500	30
3500 - 4000	22
4000 - 4500	16
4500 - 5000	7

Number of students per teacher	Number of states / U.T.
15 - 20	3
20 - 25	8
25 - 30	9
30 - 35	10
35 - 40	3
40 - 45	0
45 - 50	0
50 - 55	2

Runs scored	Number of batsmen
3000 - 4000	4
4000 - 5000	18
5000 - 6000	9
6000 - 7000	7
7000 - 8000	6
8000 - 9000	3
9000 - 10000	1
10000 - 11000	1

Number of cars	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	7	14	13	12	20	11	15	8

13.4 Median of Grouped Data

9 q

Solved Examples

Worked · 2

13.3 Eg.7 $A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and the following data was obtained. Find the median height. Height (in cm) Number of girls Less than 140 4 Less than 145 11 Less than 150 29 Less than 155 40 Less than 160 46 Less than 165 51$
13.3 Eg.8 $x$

Height (in cm)	Number of girls
Less than 140	4
Less than 145	11
Less than 150	29
Less than 155	40
Less than 160	46
Less than 165	51

Class intervals	Frequency
0 - 100	2
100 - 200	5
200 - 300	$x$
300 - 400	12
400 - 500	17
500 - 600	20
600 - 700	$y$
700 - 800	9
800 - 900	7
900 - 1000	4

Exercise 13.3

Practice · 7

Ex 13.3 Q1 $The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them. Monthly consumption (in units) Number of consumers 65 - 85 4 85 - 105 5 105 - 125 13 125 - 145 20 145 - 165 14 165 - 185 8 185 - 205 4$
Ex 13.3 Q2 $x$
Ex 13.3 Q3 $A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year. Age (in years) Number of policy holders Below 20 2 Below 25 6 Below 30 24 Below 35 45 Below 40 78 Below 45 89 Below 50 92 Below 55 98 Below 60 100$
Ex 13.3 Q4 $The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table : Length (in mm) Number of leaves 118 - 126 3 127 - 135 5 136 - 144 9 145 - 153 12 154 - 162 5 163 - 171 4 172 - 180 2 Find the median length of the leaves. (Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5.)$
Ex 13.3 Q5 $The following table gives the distribution of the life time of 400 neon lamps. Find the median life time of a lamp. Life time (in hours) Number of lamps 1500 - 2000 14 2000 - 2500 56 2500 - 3000 60 3000 - 3500 86 3500 - 4000 74 4000 - 4500 62 4500 - 5000 48$
Ex 13.3 Q6 $100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows: Number of letters 1 - 4 4 - 7 7 - 10 10 - 13 13 - 16 16 - 19 Number of surnames 630401644 Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.$
Ex 13.3 Q7 $The distribution below gives the weights of 30 students of a class. Find the median weight of the students. Weight (in kg) 40 - 45 45 - 50 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 Number of students 2386632$

Monthly consumption (in units)	Number of consumers
65 - 85	4
85 - 105	5
105 - 125	13
125 - 145	20
145 - 165	14
165 - 185	8
185 - 205	4

Class interval	Frequency
0 - 10	5
10 - 20	$x$
20 - 30	20
30 - 40	15
40 - 50	$y$
50 - 60	5
Total	60

Age (in years)	Number of policy holders
Below 20	2
Below 25	6
Below 30	24
Below 35	45
Below 40	78
Below 45	89
Below 50	92
Below 55	98
Below 60	100

Length (in mm)	Number of leaves
118 - 126	3
127 - 135	5
136 - 144	9
145 - 153	12
154 - 162	5
163 - 171	4
172 - 180	2

Life time (in hours)	Number of lamps
1500 - 2000	14
2000 - 2500	56
2500 - 3000	60
3000 - 3500	86
3500 - 4000	74
4000 - 4500	62
4500 - 5000	48

Number of letters	1 - 4	4 - 7	7 - 10	10 - 13	13 - 16	16 - 19
Number of surnames	6	30	40	16	4	4

Weight (in kg)	40 - 45	45 - 50	50 - 55	55 - 60	60 - 65	65 - 70	70 - 75
Number of students	2	3	8	6	6	3	2

What the board has asked from this chapter

Questions per paper · 67 papers · 2022 to 2026

2026

25 q

6 $\left(\dfrac{x - a}{h} = u\right)$
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Mean of Grouped Data
16 $25{\cdot}2$
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Median of Grouped Data
17 $If the mean and mode of a data are 12 and 21 respectively, then its median is :$
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Median of Grouped Data
17 $43{\cdot}4$
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Mode of Grouped Data
18 $Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is$
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Median of Grouped Data
32 $32{\cdot}5$
Median of Grouped Data
32 (a) $The median of the following data is 137. Find the values of x and y, given that total of frequencies is 68. Class Frequency 65 - 85 4 85 - 105 5 105 - 125 x 125 - 145 20 145 - 165 14 165 - 185 y 185 - 205 4$
Median of Grouped Data
32 (b) $Find mean and mode of the following distribution : Class Frequency 0 - 10 3 10 - 20 6 20 - 30 11 30 - 40 10 40 - 50 13 50 - 60 3 60 - 70 4$
Mean of Grouped Data
33 (a) $The mean of the following distribution is 53. Find the missing frequency p. Class Interval 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 Frequency 1215 p 2813 Hence, find mode of the distribution.$
Mean of Grouped Data
33 (a) $Find mean and mode of the following frequency distribution : Class : 5-15 15-25 25-35 35-45 45-55 55-65 Frequency : 112025221210$
Mean of Grouped Data
33 (b) $Compute median of the following data : Mid-value 115125135145155165175 Frequency 12152016101611$
Median of Grouped Data
33 $Find the mean and the mode of the following frequency distribution : Class Frequency 0 - 15 9 15 - 30 15 30 - 45 35 45 - 60 20 60 - 75 11 75 - 90 13 90 - 105 17$
Mean of Grouped Data
33 (b) $x$
Median of Grouped Data
33 $The marks obtained by 80 students of class X in a mock test of Mathematics are given below in the table. Find median and the mode of the data : Marks Number of Students 0 and above 80 10 and above 77 20 and above 72 30 and above 65 40 and above 55 50 and above 43 60 and above 28 70 and above 16 80 and above 10 90 and above 8 100 and above 0$
Median of Grouped Data
34 (a) $The mean of the following frequency distribution is 28. If sum of all frequencies is 100, then find the values of p and q : Class Interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency 12 p 2720 q 6$
Mean of Grouped Data
34 (a) $Find mean and mode of the following frequency distribution : Class : 10-30 30-50 50-70 70-90 90-110 110-130 130-150 Frequency : 68121014119$
Mean of Grouped Data
35 (a) $The median of the following data is 50 and sum of all frequencies is 90 : Class : 20-30 30-40 40-50 50-60 60-70 70-80 80-90 Frequency : p 152520 q 810 Find the values of p and q.$
Median of Grouped Data
34 (b) $Find median and mode of the following distribution : Class Interval 0 - 15 15 - 30 30 - 45 45 - 60 60 - 75 75 - 90 90 - 105 Frequency 15101298106$
Median of Grouped Data
34 $x$
Mode of Grouped Data
34 (b) $x$
Median of Grouped Data
35 (a) $Find the mean and mode of the following frequency distribution : Class Interval 400-450 450-500 500-550 550-600 600-650 650-700 Frequency 151820232212$
Mean of Grouped Data
35 $An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. The health insurance policies are given to persons of age 15 years and onwards, but less than 60 years. Age (in yrs) Number of policy holders 15 - 20 2 20 - 25 4 25 - 30 18 30 - 35 21 35 - 40 33 40 - 45 11 45 - 50 3 50 - 55 6 55 - 60 2 Find the modal age and median age of the policy holders.$
Mode of Grouped Data
35 (b) $Find mean and mode of the following distribution : Class : 0-15 15-30 30-45 45-60 60-75 75-90 90-105 Frequency : 4811141076$
Mean of Grouped Data
35 (b) $f_1$
Median of Grouped Data
35 $x$
Mean of Grouped Data

Class	Frequency
0 – 10	x
10 – 20	5
20 – 30	9
30 – 40	12
40 – 50	y
50 – 60	3
60 – 70	2
Total	40

Class	Frequency
65 – 85	4
85 – 105	5
105 – 125	x
125 – 145	20
145 – 165	14
165 – 185	y
185 – 205	4

Class	Frequency
0 – 10	3
10 – 20	6
20 – 30	11
30 – 40	10
40 – 50	13
50 – 60	3
60 – 70	4

Class Interval	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Frequency	12	15	p	28	13

Class :	5-15	15-25	25-35	35-45	45-55	55-65
Frequency :	11	20	25	22	12	10

Mid-value	115	125	135	145	155	165	175
Frequency	12	15	20	16	10	16	11

Class	Frequency
0 – 15	9
15 – 30	15
30 – 45	35
45 – 60	20
60 – 75	11
75 – 90	13
90 – 105	17

Class :	0-10	10-20	20-30	30-40	40-50	50-60	60-70	Total
Frequency :	$x$	5	9	12	y	3	2	40

Marks	Number of Students
0 and above	80
10 and above	77
20 and above	72
30 and above	65
40 and above	55
50 and above	43
60 and above	28
70 and above	16
80 and above	10
90 and above	8
100 and above	0

Class Interval	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Frequency	12	p	27	20	q	6

Class :	10-30	30-50	50-70	70-90	90-110	110-130	130-150
Frequency :	6	8	12	10	14	11	9

Class :	20-30	30-40	40-50	50-60	60-70	70-80	80-90
Frequency :	p	15	25	20	q	8	10

Class Interval	0 – 15	15 – 30	30 – 45	45 – 60	60 – 75	75 – 90	90 – 105
Frequency	15	10	12	9	8	10	6

Monthly Expenditure (in ₹)	No. of Families
1000-1500	24
1500-2000	40
2000-2500	33
2500-3000	28
3000-3500	$x$
3500-4000	22
4000-4500	16
4500-5000	7

Class :	0-10	10-20	20-30	30-40	40-50	50-60	Total
Frequency :	5	$x$	20	15	$y$	5	60

Class Interval	400-450	450-500	500-550	550-600	600-650	650-700
Frequency	15	18	20	23	22	12

Age (in yrs)	Number of policy holders
15 – 20	2
20 – 25	4
25 – 30	18
30 – 35	21
35 – 40	33
40 – 45	11
45 – 50	3
50 – 55	6
55 – 60	2

Class :	0-15	15-30	30-45	45-60	60-75	75-90	90-105
Frequency :	4	8	11	14	10	7	6

Class Interval	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	3	$f_1$	9	12	6	$f_2$	2

Class	Frequency
0-10	1
10-20	$x$
20-30	5
30-40	7
40-50	$y$
50-60	3
60-70	1

2025

31 q

1 $9{\cdot}6$
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Mode of Grouped Data
2 $The mean of seven observations is 17. If the mean of the first four observations is 15 and that of the last four observations is 18, then the fourth observation is :$
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Mean of Grouped Data
4 $If mode and median of given set of observations are 13 and 11 respectively, then the value of mean is :$
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Mode of Grouped Data
12 $The cumulative frequency for calculating median is obtained by adding the frequencies of all the :$
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Median of Grouped Data
12 $15x$
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Median of Grouped Data
13 $If mean and mode of given set of observations are 10 and 13 respectively, then the value of median is :$
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Mode of Grouped Data
13 $If mean and median of given set of observations are 10 and 11 respectively, then the value of mode is :$
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Mode of Grouped Data
15 $2, 9, x + 6, 2x + 3, 5, 10, 5$
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Mean of Grouped Data
15 $If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are$
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Median of Grouped Data
16 $If the maximum number of students has obtained 52 marks out of 80, then$
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Mode of Grouped Data
16 $x + y + z$
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Median of Grouped Data
17 $Following data shows the marks obtained by 100 students in a class test : Marks obtained 2029283342384325 Number of students 628241524120 The median will be the average of which two observations ?$
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Median of Grouped Data
32 $The following table shows the number of traffic challans issued in the month of April by the traffic police : Number of Challans Number of Days 0-10 3 10-20 5 20-30 10 30-40 9 40-50 2 50-60 1 Total 30 Find the ‘mean’ and ‘mode’ of the above data.$
Mean of Grouped Data
32 $p$
Median of Grouped Data
32 $During a medical checkup, height of 35 students of a class were recorded as follows : Height (in cm) 90-100 100-110 110-120 120-130 130-140 140-150 Number of Students 3245147 Find the difference between the mean height and median height.$
Median of Grouped Data
33 $The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the mean and mode of the data : Monthly Consumption (in units) Number of Consumers 65 - 85 4 85 - 105 5 105 - 125 13 125 - 145 20 145 - 165 14 165 - 185 8 185 - 205 4$
Mean of Grouped Data
34 $Find the Mean and Mode of the following data : Class Frequency 4 - 8 2 8 - 12 12 12 - 16 15 16 - 20 25 20 - 24 18 24 - 28 12 28 - 32 13 32 - 36 3$
Mean of Grouped Data
34 $Following table shows the absentees record of 40 students in an academic year : Number of Days Number of Students 2-6 11 6-10 10 10-14 7 14-18 4 18-22 4 22-26 3 26-30 1 Find the ‘mean’ and the ‘mode’ of the above data.$
Mean of Grouped Data
34 $The following table gives the daily income of 50 cab drivers of a particular city : Income (₹) 500 - 600 600 - 700 700 - 800 800 - 900 900 - 1000 No. of Drivers 12148610 Find the mean income and the modal income.$
Mode of Grouped Data
34 $Find the mean and median for the following data : Classes Frequency 5 - 15 2 15 - 25 3 25 - 35 5 35 - 45 7 45 - 55 4 55 - 65 2 65 - 75 2$
Mean of Grouped Data
34 $The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table : Length (in mm) Number of Leaves 118 - 126 3 127 - 135 5 136 - 144 9 145 - 153 12 154 - 162 5 163 - 171 4 172 - 180 2 Find the median length of the leaves.$
Median of Grouped Data
34 $x$
Median of Grouped Data
35 $Medical check-up was carried out for 35 students of a class and their weights were recorded as follows : Weight (in kg) 38-40 40-42 42-44 44-46 46-48 48-50 50-52 Number of Students 32451443 Find the difference between the mean weight and the median weight.$
Median of Grouped Data
35 $The following table shows the number of patients of different age group who were discharged from the hospital in a particular month : Age (in years) Number of Patients Discharged 5-15 6 15-25 11 25-35 21 35-45 23 45-55 14 55-65 5 Total 80 Find the ‘mean’ and the ‘mode’ of the above data.$
Mean of Grouped Data
35 $Find the missing frequency ‘f’ in the following table, if the mean of the given data is 18. Hence find the mode. Daily Allowance Number of Children 11 - 13 7 13 - 15 6 15 - 17 9 17 - 19 13 19 - 21 f 21 - 23 5 23 - 25 4$
Mean of Grouped Data
35 $x$
Median of Grouped Data
35 $Find the Mean and Mode of the following frequency distribution : Class Frequency 0 - 10 8 10 - 20 7 20 - 30 15 30 - 40 20 40 - 50 12 50 - 60 8 60 - 70 10$
Mean of Grouped Data
The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023.
Rainfall (mm) No. of Sub-divisions
200 – 400 3
400 – 600 4
600 – 800 7
800 – 1000 4
1000 – 1200 3
1200 – 1400 3
Based on the information given above, answer the following questions :
38 (i) $Write the modal class.$
Mode of Grouped Data
The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023.
Rainfall (mm) No. of Sub-divisions
200 – 400 3
400 – 600 4
600 – 800 7
800 – 1000 4
1000 – 1200 3
1200 – 1400 3
Based on the information given above, answer the following questions :
38 (ii) (a) $Find the median of the given data.$
Median of Grouped Data
The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023.
Rainfall (mm) No. of Sub-divisions
200 – 400 3
400 – 600 4
600 – 800 7
800 – 1000 4
1000 – 1200 3
1200 – 1400 3
Based on the information given above, answer the following questions :
38 (ii) (b) $Find the mean rainfall in the season.$
Mean of Grouped Data
The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023.
Rainfall (mm) No. of Sub-divisions
200 – 400 3
400 – 600 4
600 – 800 7
800 – 1000 4
1000 – 1200 3
1200 – 1400 3
Based on the information given above, answer the following questions :
38 (iii) $If a sub-division having at least 800 mm rainfall during monsoon season is considered a good rainfall sub-division, then how many sub-divisions had good rainfall ?$
Median of Grouped Data

Marks obtained	20	29	28	33	42	38	43	25
Number of students	6	28	24	15	2	4	1	20

2024

31 q

2 $\dfrac{5n}{9}$
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Mean of Grouped Data
5 $6, 7, p, 8, q, 14$
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Mean of Grouped Data
6 $2, 9, x + 6, 2x + 3, 5, 10, 5$
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Mean of Grouped Data
7 $If the difference of mode and median of a data is 24, then the difference of its median and mean is :$
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Mode of Grouped Data
8 $The mean of five numbers is 15. If we include one more number, the mean of six numbers becomes 17. The included number is :$
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Mean of Grouped Data
9 $x_1, x_2, \ldots\ldots x_n$
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Mean of Grouped Data
11 $x$
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Mean of Grouped Data
12 $If value of each observation in a data is increased by 2, then median of the new data$
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Median of Grouped Data
14 $The middle most observation of every data arranged in order is called :$
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Median of Grouped Data
16 $The mean of five observations is 15. If the mean of first three observations is 14 and that of the last three observations is 17, then the third observation is$
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Mean of Grouped Data
18 $If the mean and mode of a data are 24 and 12 respectively, then its median is :$
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Median of Grouped Data
18 $After an examination, a teacher wants to know the marks obtained by maximum number of the students in her class. She requires to calculate _____ of marks.$
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Mode of Grouped Data
30 $In a test, the marks obtained by 100 students (out of 50) are given below : Marks obtained : 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Number of students : 122334256 Find the mean marks of the students.$
Mean of Grouped Data
32 $36{\cdot}10$
Mean of Grouped Data
35 $The following table shows the ages of the patients admitted in a hospital during a year : Age (in years) 5 - 15 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 Number of patients 6112123145 Find the mode and mean of the data given above.$
Mean of Grouped Data
Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self-reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute.
Age (in years) 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54
Number of participants 62 132 96 37 13 11 10 4
From the above answer the following questions :
37 (i) $What is the lower limit of the modal class of the above data ?$
Mode of Grouped Data
BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game. The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.
Numbers announced Number of times
0-15 8
15-30 9
30-45 10
45-60 12
60-75 9
Based on the above information, answer the following :
37 (i) $Write the median class.$
Median of Grouped Data
Activities like running or cycling reduce stress and the risk of mental disorder like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :
Time (in seconds) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
Number of students 8 10 13 6 3
Based on the above, answer the following questions :
37 (i) $What is the median class of the above given data ?$
Median of Grouped Data
Activities like running or cycling reduce stress and the risk of mental disorder like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :
Time (in seconds) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
Number of students 8 10 13 6 3
Based on the above, answer the following questions :
37 (ii) (a) $Find the mean time taken by the students to finish the race.$
Mean of Grouped Data
Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self-reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute.
Age (in years) 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54
Number of participants 62 132 96 37 13 11 10 4
From the above answer the following questions :
37 (ii) (a) $Find the median class of the above data.$
Median of Grouped Data
BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game. The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.
Numbers announced Number of times
0-15 8
15-30 9
30-45 10
45-60 12
60-75 9
Based on the above information, answer the following :
37 (iii) (a) $Find median of the given data.$
Median of Grouped Data
Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self-reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute.
Age (in years) 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54
Number of participants 62 132 96 37 13 11 10 4
From the above answer the following questions :
37 (ii) (b) $Find the number of participants of age less than 50 years who undergo vocational training.$
Median of Grouped Data
Activities like running or cycling reduce stress and the risk of mental disorder like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :
Time (in seconds) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
Number of students 8 10 13 6 3
Based on the above, answer the following questions :
37 (ii) (b) $Find the mode of the above given data.$
Mode of Grouped Data
Activities like running or cycling reduce stress and the risk of mental disorder like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :
Time (in seconds) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
Number of students 8 10 13 6 3
Based on the above, answer the following questions :
37 (iii) $How many students took time less than 60 seconds ?$
Median of Grouped Data
BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. The participant cancels the number on the card when called out a number written on the ball selected at random. Whosoever cancels all the numbers on his/her card, says BINGO and wins the game. The table given below, shows the data of one such game where 48 balls were used before Tara said 'BINGO'.
Numbers announced Number of times
0-15 8
15-30 9
30-45 10
45-60 12
60-75 9
Based on the above information, answer the following :
37 (iii) (b) $Find mode of the given data.$
Mode of Grouped Data
Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self-reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute.
Age (in years) 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54
Number of participants 62 132 96 37 13 11 10 4
From the above answer the following questions :
37 (iii) $Give the empirical relationship between mean, median and mode.$
Median of Grouped Data
Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :
Time (in seconds) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
Number of students 8 10 13 6 3
Based on the above, answer the following questions :
38 (i) $What is the median class of the above given data ?$
Median of Grouped Data
In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey. Observe the pie chart and answer the following questions :
38 (ii) $Which is most favourite mode of transport and how many people used it ?$
Mode of Grouped Data
Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :
Time (in seconds) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
Number of students 8 10 13 6 3
Based on the above, answer the following questions :
38 (ii) (a) $Find the mean time taken by the students to finish the race.$
Mean of Grouped Data
Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :
Time (in seconds) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
Number of students 8 10 13 6 3
Based on the above, answer the following questions :
38 (ii) (b) $Find the mode of the above given data.$
Mode of Grouped Data
Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run 100 m, was noted as follows :
Time (in seconds) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
Number of students 8 10 13 6 3
Based on the above, answer the following questions :
38 (iii) $How many students took time less than 60 seconds ?$
Median of Grouped Data

2023

18 q

4 $If the mean and the mode of a distribution are 15 and 18 respectively, then the median of the distribution is :$
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Median of Grouped Data
6 $The empirical relation between the mode, median and mean of a distribution is :$
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Median of Grouped Data
10 $If the mean and the median of a data are 12 and 15 respectively, then its mode is :$
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Median of Grouped Data
11 $The distribution below gives the marks obtained by 80 students on a test : Marks Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Number of Students 31227577580 The modal class of this distribution is :$
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Mode of Grouped Data
11 $For the following distribution : Class 0-5 5-10 10-15 15-20 20-25 Frequency 101512209 The sum of lower limits of median class and modal class is :$
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Median of Grouped Data
15 $If the value of each observation of a statistical data is increased by 3, then the mean of the data$
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Mean of Grouped Data
15 $For the following distribution : Marks Below 102030405060 Number of Students 31227577580 The modal class is :$
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Mode of Grouped Data
18 $If every term of the statistical data consisting of n terms is decreased by 2, then the mean of the data :$
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Mean of Grouped Data
26 $Find the mean of the following distribution : Classes 0 - 15 15 - 30 30 - 45 45 - 60 60 - 75 75 - 90 Frequency 17201821159$
Mean of Grouped Data
31 $Find the mean of the following frequency distribution : Classes 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 50 - 55 55 - 60 Frequency 1422166534$
Mean of Grouped Data
32 $The mode of the following frequency distribution is 55. Find the missing frequencies ‘a’ and ‘b’. Class Interval 0 - 15 15 - 30 30 - 45 45 - 60 60 - 75 75 - 90 Total Frequency 67 a 1510 b 51$
Mode of Grouped Data
34 $A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mean and median of the following data. Number of cars Frequency (periods) 0 - 10 7 10 - 20 14 20 - 30 13 30 - 40 12 40 - 50 20 50 - 60 11 60 - 70 15 70 - 80 8$
Mean of Grouped Data
35 $x$
Median of Grouped Data
35 $x$
Mean of Grouped Data
India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 :
Rainfall (mm) Number of Sub-divisions
200-400 2
400-600 4
600-800 7
800-1000 4
1000-1200 2
1200-1400 3
1400-1600 1
1600-1800 1
Based on the above information, answer the following questions :
37 (I) $Write the modal class.$
Mode of Grouped Data
India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 :
Rainfall (mm) Number of Sub-divisions
200-400 2
400-600 4
600-800 7
800-1000 4
1000-1200 2
1200-1400 3
1400-1600 1
1600-1800 1
Based on the above information, answer the following questions :
37 (II) $Find the median of the given data.$
Median of Grouped Data
India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 :
Rainfall (mm) Number of Sub-divisions
200-400 2
400-600 4
600-800 7
800-1000 4
1000-1200 2
1200-1400 3
1400-1600 1
1600-1800 1
Based on the above information, answer the following questions :
37 (II) OR $Find the mean rainfall in this season.$
Mean of Grouped Data
India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 :
Rainfall (mm) Number of Sub-divisions
200-400 2
400-600 4
600-800 7
800-1000 4
1000-1200 2
1200-1400 3
1400-1600 1
1600-1800 1
Based on the above information, answer the following questions :
37 (III) $If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub-divisions had good rainfall ?$
Median of Grouped Data

2022

14 q

1 $The mode of a grouped frequency distribution is 75 and the modal class is 65-80. The frequency of the class preceding the modal class is 6 and the frequency of the class succeeding the modal class is 8. Find the frequency of the modal class.$
Mode of Grouped Data
3 $Find the mode of the given frequency distribution : Class Frequency 15 - 25 6 25 - 35 11 35 - 45 22 45 - 55 23 55 - 65 14 65 - 75 5$
Mode of Grouped Data
4 $Find the mean of the following frequency distribution : Class 1 - 5 5 - 9 9 - 13 13 - 17 Frequency 4876$
Mean of Grouped Data
4 $Find the mode of the following frequency distribution : Class 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency 151012174$
Mode of Grouped Data
5 $x$
Mode of Grouped Data
7 $34{\cdot}5$
Median of Grouped Data
9 (a) $The mean of the following frequency distribution is 25. Find the value of f. Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 51815 f 6$
Mean of Grouped Data
9 $The weights (in kg) of 50 wild animals of a National Park were recorded and the following data was obtained : Weight (in kg) Number of animals 100 - 110 4 110 - 120 12 120 - 130 23 130 - 140 8 140 - 150 3 Find the mean weight (in kg) of animals, using assumed mean method.$
Mean of Grouped Data
9 (b) $Find the mean of the following data using assumed mean method : Class 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 Frequency 87101312$
Mean of Grouped Data
10 $For the following frequency distribution, find the median : Class Frequency 1400 - 1550 6 1550 - 1700 13 1700 - 1850 25 1850 - 2000 10$
Median of Grouped Data
10 $Heights of 50 students of class X of a school are recorded and following data is obtained : Height (in cm) 130-135 135-140 140-145 145-150 150-155 155-160 Number of Students 411127106 Find the median height of the students.$
Median of Grouped Data
10 $Following is the daily expenditure on lunch by 30 employees of a company : Daily Expenditure (in Rupees) Number of Employees 100 - 120 8 120 - 140 3 140 - 160 8 160 - 180 6 180 - 200 5 Find the mean daily expenditure of the employees.$
Mean of Grouped Data
Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not even make our body healthy but also achieve inner peace and calmness. The International Yoga Day is celebrated on $21^{\text{st}}$ of June every year since 2015. To promote Yoga, Green park society in Pune organised a 7-day Yoga camp in their society. The number of people of different age groups who enrolled for this camp is given as follows :
Age Group 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65 65 – 75 75 – 85
Number of People 8 10 15 25 40 24 18
Based on the above, find the following :
13 (a) $Find the median age of people enrolled for the camp.$
Median of Grouped Data
Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not even make our body healthy but also achieve inner peace and calmness. The International Yoga Day is celebrated on $21^{\text{st}}$ of June every year since 2015. To promote Yoga, Green park society in Pune organised a 7-day Yoga camp in their society. The number of people of different age groups who enrolled for this camp is given as follows :
Age Group 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65 65 – 75 75 – 85
Number of People 8 10 15 25 40 24 18
Based on the above, find the following :
13 (b) $x$
Mean of Grouped Data

The 10 board questions to practise first

The questions the board asked again come first, most asked first. Each one says how often and when.

Question 1
Asked 4 times: 2023*, 2024*, 2025*, 2026 (* = numbers or wording changed that year)
16 $25{\cdot}2$
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Question 2
Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)
34 $x$
Question 3
Asked 2 times: 2024, 2025
35 $The following table shows the number of patients of different age group who were discharged from the hospital in a particular month : Age (in years) Number of Patients Discharged 5-15 6 15-25 11 25-35 21 35-45 23 45-55 14 55-65 5 Total 80 Find the ‘mean’ and the ‘mode’ of the above data.$
Question 4
Asked 2 times: 2024, 2025
15 $2, 9, x + 6, 2x + 3, 5, 10, 5$
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Question 5 (case study, 4 parts)
Asked 2 times: 2023*, 2025 (* = numbers or wording changed that year)
The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023.
Rainfall (mm) No. of Sub-divisions
200 – 400 3
400 – 600 4
600 – 800 7
800 – 1000 4
1000 – 1200 3
1200 – 1400 3
Based on the information given above, answer the following questions :
38 (i) $Write the modal class.$
38 (ii) (a) $Find the median of the given data.$
38 (ii) (b) $Find the mean rainfall in the season.$
38 (iii) $If a sub-division having at least 800 mm rainfall during monsoon season is considered a good rainfall sub-division, then how many sub-divisions had good rainfall ?$
Question 6
Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)
2 $The mean of seven observations is 17. If the mean of the first four observations is 15 and that of the last four observations is 18, then the fourth observation is :$
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Question 7
Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)
35 $Find the missing frequency ‘f’ in the following table, if the mean of the given data is 18. Hence find the mode. Daily Allowance Number of Children 11 - 13 7 13 - 15 6 15 - 17 9 17 - 19 13 19 - 21 f 21 - 23 5 23 - 25 4$
Question 8
Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)
32 $The mode of the following frequency distribution is 55. Find the missing frequencies ‘a’ and ‘b’. Class Interval 0 - 15 15 - 30 30 - 45 45 - 60 60 - 75 75 - 90 Total Frequency 67 a 1510 b 51$
Question 9
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2025
15 $If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are$
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Question 10
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026
35 (b) $Find mean and mode of the following distribution : Class : 0-15 15-30 30-45 45-60 60-75 75-90 90-105 Frequency : 4811141076$

Length (in mm)	Number of Leaves
118 – 126	3
127 – 135	5
136 – 144	9
145 – 153	12
154 – 162	5
163 – 171	4
172 – 180	2

Number of lions	Number of regions
0 – 100	2
100 – 200	5
200 – 300	9
300 – 400	12
400 – 500	$x$
500 – 600	20
600 – 700	15
700 – 800	9
800 – 900	$y$
900 – 1000	2
	100

Daily Allowance	Number of Children
11 – 13	7
13 – 15	6
15 – 17	9
17 – 19	13
19 – 21	f
21 – 23	5
23 – 25	4

Weight (in kg)	Number of animals
100 – 110	4
110 – 120	12
120 – 130	23
130 – 140	8
140 – 150	3

Daily Expenditure (in Rupees)	Number of Employees
100 – 120	8
120 – 140	3
140 – 160	8
160 – 180	6
180 – 200	5

Class	Frequency
4 – 8	2
8 – 12	12
12 – 16	15
16 – 20	25
20 – 24	18
24 – 28	12
28 – 32	13
32 – 36	3

Classes	Frequency
5 – 15	2
15 – 25	3
25 – 35	5
35 – 45	7
45 – 55	4
55 – 65	2
65 – 75	2

Rainfall (mm)	No. of Sub-divisions
200 – 400	3
400 – 600	4
600 – 800	7
800 – 1000	4
1000 – 1200	3
1200 – 1400	3

Rainfall (mm)	Number of Sub-divisions
200-400	2
400-600	4
600-800	7
800-1000	4
1000-1200	2
1200-1400	3
1400-1600	1
1600-1800	1

13.2 Mean of Grouped Data

Solved Examples

Exercise 13.1

13.3 Mode of Grouped Data

Solved Examples

Exercise 13.2

13.4 Median of Grouped Data

Solved Examples

Exercise 13.3

What the board has asked from this chapter

2026

2025

2024

2023

2022

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5 (case study, 4 parts)

Question 6

Question 7

Question 8

Question 9

Question 10