Algebra · 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. · 80 questions

Mean of grouped data - Direct method

3 q

Direct method

Worked · 1

Direct method Ex.1 $The following table shows the frequency distribution of the time required for each worker to complete a work. From the table find the mean time required to complete the job for a worker. Time (Hrs.) for each to complete the work 15-19 20-24 25-29 30-34 35-39 No. of workers 10151285$

Time (Hrs.) for each to complete the work	15-19	20-24	25-29	30-34	35-39
No. of workers	10	15	12	8	5

Solved Examples

Worked · 2

Direct method SolvedEx.1 $The percentage of marks of 50 students in a test is given in the following table. Find the mean of the percentage. Percentage of marks 0-20 20-40 40-60 60-80 80-100 No. of students 3715205$
Direct method SolvedEx.2 $^\circ$

Percentage of marks	0-20	20-40	40-60	60-80	80-100
No. of students	3	7	15	20	5

Temperature ( $^\circ$ C)	24-28	28-32	32-36	36-40	40-44
No. of towns	4	5	7	8	6

Mean of grouped data - Assumed mean method

2 q

Assumed mean method

Worked · 1

Assumed mean Ex.1 $The daily sale of 100 vegetable vendors is given in the following table. Find the mean of the sale by assumed mean method. Daily sale (Rupees) 1000-1500 1500-2000 2000-2500 2500-3000 No. of vendors 15203530$

Daily sale (Rupees)	1000-1500	1500-2000	2000-2500	2500-3000
No. of vendors	15	20	35	30

Solved Examples

Worked · 1

Assumed mean SolvedEx.1 $The following table shows the frequency table of daily wages of 50 workers in a trading company. Find the mean wages of a worker, by assumed mean method. Daily Wages (Rs) 200-240 240-280 280-320 320-360 360-400 Frequency 51015128$

Daily Wages (Rs)	200-240	240-280	280-320	320-360	360-400
Frequency	5	10	15	12	8

Mean of grouped data - Step deviation method

2 q

Step deviation method

Worked · 1

Step deviation Ex.1 $The amount invested in health insurance by 100 families is given in the following frequency table. Find the mean of investments using step deviation method. Amount invested (₹) 800-1200 1200-1600 1600-2000 2000-2400 2400-2800 2800-3200 No. of families 3152025307$

Amount invested (₹)	800-1200	1200-1600	1600-2000	2000-2400	2400-2800	2800-3200
No. of families	3	15	20	25	30	7

Solved Example

Worked · 1

Step deviation SolvedEx.1 $The following table shows the funds collected by 50 students for flood affected people. Find the mean of the funds. Fund (Rupees) 0-500 500-1000 1000-1500 1500-2000 2000-2500 2500-3000 No. of students 24241811$

Fund (Rupees)	0-500	500-1000	1000-1500	1500-2000	2000-2500	2500-3000
No. of students	2	4	24	18	1	1

Practice set 6.1

6 q

Ex 6.1 Q.1 $The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method. Time (hrs.) 0-2 2-4 4-6 6-8 8-10 No. of students 71812103$
Ex 6.1 Q.2 $In the following table, the toll paid by drivers and the number of vehicles is shown. Find the mean of the toll by 'assumed mean' method. Toll (Rupees) 300-400 400-500 500-600 600-700 700-800 No. of vehicles 801101207040$
Ex 6.1 Q.3 $A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method. Milk Sold (Litre) 1-2 2-3 3-4 4-5 5-6 No. of Customers 17131073$
Ex 6.1 Q.4 $A frequency distribution table for the production of oranges of some farm owners is given below. Find the mean production of oranges by 'assumed mean' method. Production (Thousand rupees) 25-30 30-35 35-40 40-45 45-50 No. of farm owners 2025151010$
Ex 6.1 Q.5 $A frequency distribution of funds collected by 120 workers in a company for the drought affected people are given in the following table. Find the mean of the funds by 'step deviation' method. Fund (Rupees) 0-500 500-1000 1000-1500 1500-2000 2000-2500 No. of workers 3528321510$
Ex 6.1 Q.6 $The following table gives the information of frequency distribution of weekly wages of 150 workers of a company. Find the mean of the weekly wages by 'step deviation' method. Weekly wages (Rupees) 1000-2000 2000-3000 3000-4000 4000-5000 No. of workers. 25455030$

Time (hrs.)	0-2	2-4	4-6	6-8	8-10
No. of students	7	18	12	10	3

Toll (Rupees)	300-400	400-500	500-600	600-700	700-800
No. of vehicles	80	110	120	70	40

Milk Sold (Litre)	1-2	2-3	3-4	4-5	5-6
No. of Customers	17	13	10	7	3

Production (Thousand rupees)	25-30	30-35	35-40	40-45	45-50
No. of farm owners	20	25	15	10	10

Fund (Rupees)	0-500	500-1000	1000-1500	1500-2000	2000-2500
No. of workers	35	28	32	15	10

Weekly wages (Rupees)	1000-2000	2000-3000	3000-4000	4000-5000
No. of workers.	25	45	50	30

Median of grouped data

1 q

Solved Example

Worked · 1

Median SolvedEx.1 $The following table shows frequency distribution of marks of 100 students of 10th class which they obtained in a practice examination. Find the median of the marks. Marks in exam 0-20 20-40 40-60 60-80 80-100 No. of students 42030406$

Marks in exam	0-20	20-40	40-60	60-80	80-100
No. of students	4	20	30	40	6

Median from a cumulative frequency table

2 q

Solved Examples

Worked · 2

Median cf SolvedEx.1 $Observe the following frequency distribution table. It shows the distances travelled by 60 public transport buses in a day. Find the median of the distance travelled. Daily distance travelled (in Km) 200-209 210-219 220-229 230-239 240-249 No. of buses 41426106$
Median cf SolvedEx.2 $The following table shows the ages of persons who visited a museum on a certain day. Find the median age of the persons visiting the museum. Age (Years) No. of persons Less than 10 3 Less than 20 10 Less than 30 22 Less than 40 40 Less than 50 54 Less than 60 71$

Daily distance travelled (in Km)	200-209	210-219	220-229	230-239	240-249
No. of buses	4	14	26	10	6

Age (Years)	No. of persons
Less than 10	3
Less than 20	10
Less than 30	22
Less than 40	40
Less than 50	54
Less than 60	71

Practice set 6.2

4 q

Ex 6.2 Q.1 $The following table shows classification of number of workers and the number of hours they work in a software company. Find the median of the number of hours they work. Daily No. of hours 8-10 10-12 12-14 14-16 Number of workers 15050030050$
Ex 6.2 Q.2 $The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of data. No. of Mangoes 50-100 100-150 150-200 200-250 250-300 No. of trees 3330908017$
Ex 6.2 Q.3 $The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data. Average Speed of Vehicles (Km/hr) 60-64 64-69 70-74 75-79 79-84 84-89 No. of vehicles 10345585106$
Ex 6.2 Q.4 $The production of electric bulbs in different factories is shown in the following table. Find the median of the productions. No. of bulbs produced (Thousands) 30-40 40-50 50-60 60-70 70-80 80-90 90-100 No. of factories 12352015878$

Daily No. of hours	8-10	10-12	12-14	14-16
Number of workers	150	500	300	50

No. of Mangoes	50-100	100-150	150-200	200-250	250-300
No. of trees	33	30	90	80	17

Average Speed of Vehicles (Km/hr)	60-64	64-69	70-74	75-79	79-84	84-89
No. of vehicles	10	34	55	85	10	6

No. of bulbs produced (Thousands)	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. of factories	12	35	20	15	8	7	8

Mode of grouped data

2 q

Solved Examples

Worked · 2

Mode SolvedEx.1 $The classification of children according to their ages, playing on a ground is shown in the following table. Find the mode of ages of the children. Age-group of children (Yrs) 6-8 8-10 10-12 12-14 14-16 No. of children 4358704227$
Mode SolvedEx.2 $The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. Find the mode of the volume. Petrol filled (Litre) 1-3 4-6 7-9 10-12 13-15 No. of vehicle 3340271812$

Age-group of children (Yrs)	6-8	8-10	10-12	12-14	14-16
No. of children	43	58	70	42	27

Petrol filled (Litre)	1-3	4-6	7-9	10-12	13-15
No. of vehicle	33	40	27	18	12

Practice set 6.3

4 q

Ex 6.3 Q.1 $The following table shows the information regarding the milk collected from farmers on a milk collection centre and the content of fat in the milk, measured by a lactometer. Find the mode of fat content. Content of fat (%) 2-3 3-4 4-5 5-6 6-7 Milk collected (Litre) 3070806020$
Ex 6.3 Q.2 $Electricity used by some families is shown in the following table. Find the mode for use of electricity. Use of electricity (Unit) 0-20 20-40 40-60 60-80 80-100 100-120 No. of families 1350701008017$
Ex 6.3 Q.3 $Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk. Milk (Litre) 1-3 3-5 5-7 7-9 9-11 11-13 No. of hotels 7515203518$
Ex 6.3 Q.4 $The following frequency distribution table gives the ages of 200 patients treated in a hospital in a week. Find the mode of ages of the patients. Age (years) Less than 5 5-9 10-14 15-19 20-24 25-29 No. of patients 383250362420$

Content of fat (%)	2-3	3-4	4-5	5-6	6-7
Milk collected (Litre)	30	70	80	60	20

Use of electricity (Unit)	0-20	20-40	40-60	60-80	80-100	100-120
No. of families	13	50	70	100	80	17

Milk (Litre)	1-3	3-5	5-7	7-9	9-11	11-13
No. of hotels	7	5	15	20	35	18

Age (years)	Less than 5	5-9	10-14	15-19	20-24	25-29
No. of patients	38	32	50	36	24	20

Histogram

1 q

Histogram Ex.1 $The table below shows the net asset value (NAV) per unit of mutual funds of some companies. Draw a histogram representing the information. NAV (₹) 8-9 10-11 12-13 14-15 16-17 No. of mutual funds 2040302515$

NAV (₹)	8-9	10-11	12-13	14-15	16-17
No. of mutual funds	20	40	30	25	15

Practice set 6.4

4 q

Ex 6.4 Q.1 $Draw a histogram of the following data. Height of student (cm) 135-140 140-145 145-150 150-155 No. of students 412168$
Ex 6.4 Q.2 $The table below shows the yield of jowar per acre. Show the data by histogram. Yield per acre (quintal) 2-3 4-5 6-7 8-9 10-11 No. of farmers 3050554020$
Ex 6.4 Q.3 $In the following table, the investment made by 210 families is shown. Present it in the form of a histogram. Investment (Thousand Rupees) 10-15 15-20 20-25 25-30 30-35 No. of families 3050605515$
Ex 6.4 Q.4 $Time alloted for the preparation of an examination by some students is shown in the table. Draw a histogram to show the information. Time (minutes) 60-80 80-100 100-120 120-140 140-160 No. of students 1420242216$

Height of student (cm)	135-140	140-145	145-150	150-155
No. of students	4	12	16	8

Yield per acre (quintal)	2-3	4-5	6-7	8-9	10-11
No. of farmers	30	50	55	40	20

Investment (Thousand Rupees)	10-15	15-20	20-25	25-30	30-35
No. of families	30	50	60	55	15

Time (minutes)	60-80	80-100	100-120	120-140	140-160
No. of students	14	20	24	22	16

Frequency polygon

2 q

Solved Examples

Worked · 2

Frequency polygon SolvedEx.1 $Answer the following questions based on the frequency polygon given in the adjacent figure (fig 6.4). (1) Write frequency of the class 50-60. (2) State the class whose frequency is 14. (3) State the class whose class mark is 55. (4) Write the class in which the frequency is maximum. (5) Write the classes whose frequencies are zero.$
Frequency polygon SolvedEx.2 $The following table shows the weights of children and the number of children. Draw a frequency polygon showing the information. Weight of children (kg) 18-19 19-20 20-21 21-22 22-23 23-24 No. of children 4131519176$

Weight of children (kg)	18-19	19-20	20-21	21-22	22-23	23-24
No. of children	4	13	15	19	17	6

Practice set 6.5

7 q

Observe the adjacent frequency polygon (fig 6.6) and write the answers of the following questions.
Ex 6.5 Q.1(1) $Which class has the maximum number of students?$
Ex 6.5 Q.1(2) $Write the classes having zero frequency.$
Ex 6.5 Q.1(3) $What is the class-mark of the class, having frequency of 50 students?$
Ex 6.5 Q.1(4) $Write the lower and upper class limits of the class whose class mark is 85.$
Ex 6.5 Q.1(5) $How many students are in the class 80-90?$
Ex 6.5 Q.2 $Show the following data by a frequency polygon. Electricity bill (₹) 0-200 200-400 400-600 600-800 800-1000 Families 240300450350160$
Ex 6.5 Q.3 $The following table shows the classification of percentages of marks of students and the number of students. Draw a frequency polygon from the table. Result (Percentage) 30-40 40-50 50-60 60-70 70-80 80-90 90-100 No. of students 733456547185$

Electricity bill (₹)	0-200	200-400	400-600	600-800	800-1000
Families	240	300	450	350	160

Result (Percentage)	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. of students	7	33	45	65	47	18	5

Pie diagram

3 q

To read a Pie diagram

Worked · 1

Pie diagram Ex.1 $138^\circ$

Solved Examples

Worked · 2

Pie diagram SolvedEx.1 $In a bicycle shop, number of bicycles purchased and choice of their colours was as follows. Find the measures of sectors of a circle to show the information by a pie diagram. Colour White Black Blue Grey Red Number of bicycles 109674$
Pie diagram SolvedEx.2 $The following table shows the daily supply of electricity to different places in a town. Show the information by a pie diagram. Places Factories Houses Roads Shops Offices Others Supply of electricity (Thousand units) 24147564$

Colour	White	Black	Blue	Grey	Red
Number of bicycles	10	9	6	7	4

Places	Factories	Houses	Roads	Shops	Offices	Others
Supply of electricity (Thousand units)	24	14	7	5	6	4

Practice set 6.6

11 q

Ex 6.6 Q.1 $The age group and number of persons, who donated blood in a blood donation camp is given below. Draw a pie diagram from it. Age group (Yrs) 20-25 25-30 30-35 35-40 No. of persons 80603525$
Ex 6.6 Q.2 $The marks obtained by a student in different subjects are shown. Draw a pie diagram showing the information. Subject English Marathi Science Mathematics Social science Hindi Marks 507080906050$
Ex 6.6 Q.3 $In a tree plantation programme, the number of trees planted by students of different classes is given in the following table. Draw a pie diagram showing the information. Standard 5th 6th 7th 8th 9th 10th No. of trees 405075507075$
Ex 6.6 Q.4 $The following table shows the percentages of demands for different fruits registered with a fruit vendor. Show the information by a pie diagram. Fruits Mango Sweet lime Apples Cheeku Oranges Percentages of demand 3015252010$
The pie diagram in figure 6.13 shows the proportions of different workers in a town. Answer the following questions with its help. The central angles of the sectors are: Production $90^\circ$ , Construction $72^\circ$ , Hotels $72^\circ$ , Food $48^\circ$ , Administration (Admin) $36^\circ$ , Agriculture $24^\circ$ , Electricity $18^\circ$ .
Ex 6.6 Q.5(1) $If the total workers is 10,000; how many of them are in the field of construction?$
Ex 6.6 Q.5(2) $How many workers are working in the administration?$
Ex 6.6 Q.5(3) $What is the percentage of workers in production?$
The annual investments of a family are shown in the adjacent pie diagram (fig 6.14). Answer the following questions based on it. The central angles of the sectors are: Immovable Property $120^\circ$ , Deposit in bank $90^\circ$ , Shares $60^\circ$ , Mutual fund $60^\circ$ , Post $30^\circ$ .
Ex 6.6 Q.6(1) $If the investment in shares is ₹ 2000/-, find the total investment.$
Ex 6.6 Q.6(2) $How much amount is deposited in bank?$
Ex 6.6 Q.6(3) $How much more money is invested in immovable property than in mutual fund?$
Ex 6.6 Q.6(4) $How much amount is invested in post?$

Age group (Yrs)	20-25	25-30	30-35	35-40
No. of persons	80	60	35	25

Subject	English	Marathi	Science	Mathematics	Social science	Hindi
Marks	50	70	80	90	60	50

Standard	5th	6th	7th	8th	9th	10th
No. of trees	40	50	75	50	70	75

Fruits	Mango	Sweet lime	Apples	Cheeku	Oranges
Percentages of demand	30	15	25	20	10

Miscellaneous Problems - 6

26 q

Find the correct answer from the alternatives given.
PS6 Q.1(1) $The persons of O- blood group are 40%. The classification of persons based on blood groups is to be shown by a pie diagram. What should be the measures of angle for the persons of O- blood group?$
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PS6 Q.1(2) $75^\circ$
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PS6 Q.1(3) $Cumulative frequencies in a grouped frequency table are useful to find . . .$
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PS6 Q.1(4) $\overline{X} = A + \dfrac{\Sigma f_i u_i}{\Sigma f_i} \times h$
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PS6 Q.1(5) $Distance Covered per litre (km) 12-14 14-16 16-18 18-20 No. of cars 1112207 The median of the distances covered per litre shown in the above data is in the group . . . . . .$
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PS6 Q.1(6) $No. of trees planted by each student 1-3 4-6 7-9 10-12 No. of students 7864 The above data is to be shown by a frequency polygon. The coordinates of the points to show number of students in the class 4-6 are . . . .$
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PS6 Q.2 $The following table shows the income of farmers in a grape season. Find the mean of their income. Income (Thousand Rupees) 20-30 30-40 40-50 50-60 60-70 70-80 Farmers 101115161814$
PS6 Q.3 $The loans sanctioned by a bank for construction of farm ponds are shown in the following table. Find the mean of the loans. Loan (Thousand Rupees) 40-50 50-60 60-70 70-80 80-90 No. of farm ponds 132024367$
PS6 Q.4 $The weekly wages of 120 workers in a factory are shown in the following frequency distribution table. Find the mean of the weekly wages by 'assumed mean' method. Weekly wages (Rupees) 0-2000 2000-4000 4000-6000 6000-8000 No. of workers 15355020$
PS6 Q.5 $The following frequency distribution table shows the amount of aid given to 50 flood affected families. Find the mean of the amount of aid. Amount of aid (Thosand rupees) 50-60 60-70 70-80 80-90 90-100 No. of families 7132064$
PS6 Q.6 $The distances covered by 250 public transport buses in a day is shown in the following frequency distribution table. Find the median of the distances. Distance (km) 200-210 210-220 220-230 230-240 240-250 No. of buses 4060805020$
PS6 Q.7 $The prices of different articles and demand for them is shown in the following frequency distribution table. Find the median of the prices. Price (Rupees) 20 less than 20-40 40-60 60-80 80-100 No. of articles 140100806020$
PS6 Q.8 $The following frequency table shows the demand for a sweet and the number of customers. Find the mode of demand of sweet. Weight of sweet (gram) 0-250 250-500 500-750 750-1000 1000-1250 No. of customers 1060252015$
PS6 Q.9 $Draw a histogram for the following frequency distribution. Use of electricity (Unit) 50-70 70-90 90-110 110-130 130-150 150-170 No. of families 150400460540600350$
PS6 Q.10 $In a handloom factory different workers take different periods of time to weave a saree. The number of workers and their required periods are given below. Present the information by a frequency polygon. No. of days 8-10 10-12 12-14 14-16 16-18 18-20 No. of workers 51630403514$
PS6 Q.11 $The time required for students to do a science experiment and the number of students is shown in the following grouped frequency distribution table. Show the information by a histogram and also by a frequency polygon. Time required for experiment (minutes) 20-22 22-24 24-26 26-28 28-30 30-32 No. of students 81622181412$
PS6 Q.12 $Draw a frequency polygon for the following grouped frequency distribution table. Age of the donor (Yrs.) 20-24 25-29 30-34 35-39 40-44 45-49 No. of blood doners 384635241512$
PS6 Q.13 $The following table shows the average rainfall in 150 towns. Show the information by a frequency polygon. Average rainfall (cm) 0-20 20-40 40-60 60-80 80-100 No. of towns 1412364840$
Observe the adjacent pie diagram (fig 6.15). It shows the percentages of number of vehicles passing a signal in a town between 8 am and 10 am. The sectors are labelled: Cars 30%, Tempos 12%, Buses 8%, Auto-rikshaws 10%, Two wheelers 40%.
PS6 Q.14(1) $Find the central angle for each type of vehicle.$
PS6 Q.14(2) $If the number of two-wheelers is 1200, find the number of all vehicles.$
PS6 Q.15 $The following table shows causes of noise pollution. Show it by a pie diagram. Construction Traffic Aircraft take offs Industry Trains 10% 50% 9% 20% 11%$
A survey of students was made to know which game they like. The data obtained in the survey is presented in the adjacent pie diagram (fig 6.16), whose sectors have central angles Cricket $81^\circ$ , Football $63^\circ$ , Hockey $54^\circ$ , Other $72^\circ$ , Kho-kho $45^\circ$ and Kabaddi $45^\circ$ . If the total number of students are 1000,
PS6 Q.16(1) $How many students like cricket?$
PS6 Q.16(2) $How many students like football?$
PS6 Q.16(3) $How many students prefer other games?$
PS6 Q.17 $Medical check up of 180 women was conducted in a health centre in a village. 50 of them were short of haemoglobin, 10 suffered from cataract and 25 had respiratory disorders. The remaining women were healthy. Show the information by a pie diagram.$
PS6 Q.18 $On an environment day, students in a school planted 120 trees under plantation project. The information regarding the project is shown in the following table. Show it by a pie diagram. Tree name Karanj Behada Arjun Bakul Kadunimb No. of trees 2028242226$

Distance Covered per litre (km)	12-14	14-16	16-18	18-20
No. of cars	11	12	20	7

No. of trees planted by each student	1-3	4-6	7-9	10-12
No. of students	7	8	6	4

Income (Thousand Rupees)	20-30	30-40	40-50	50-60	60-70	70-80
Farmers	10	11	15	16	18	14

Loan (Thousand Rupees)	40-50	50-60	60-70	70-80	80-90
No. of farm ponds	13	20	24	36	7

Weekly wages (Rupees)	0-2000	2000-4000	4000-6000	6000-8000
No. of workers	15	35	50	20

Amount of aid (Thosand rupees)	50-60	60-70	70-80	80-90	90-100
No. of families	7	13	20	6	4

Distance (km)	200-210	210-220	220-230	230-240	240-250
No. of buses	40	60	80	50	20

Price (Rupees)	20 less than	20-40	40-60	60-80	80-100
No. of articles	140	100	80	60	20

Weight of sweet (gram)	0-250	250-500	500-750	750-1000	1000-1250
No. of customers	10	60	25	20	15

Use of electricity (Unit)	50-70	70-90	90-110	110-130	130-150	150-170
No. of families	150	400	460	540	600	350

What the board has asked from this chapter

Questions per paper · 12 papers · 2016 to 2026

June 2026

5 q

Q1(A)(iv) $40\%$
Tap an option to check your answer.
Pictorial Representation of Statistical Data
Q1(B)(iv) $\sum x_i f_i = 1265$
Mean, Median and Mode of Grouped Data
Q3(B)(iii) $काही कुटुंबांचा मासिक वीजवापर पुढील वर्गीकृत वारंवारता सारणीत दिला आहे. त्यावरून वीजवापराचे बहुलक काढा. वीजवापर (यूनिटस्) कुटुंबाची संख्या 0-20 13 20-40 50 40-60 70 60-80 100 80-100 80 100-120 17 Electricity used by some families is shown in the following table. Find the mode of electricity used. Use of Electricity (Units) No. of Families 0-20 13 20-40 50 40-60 70 60-80 100 80-100 80 100-120 17$
Mean, Median and Mode of Grouped Data
Q4(i) $एका परीक्षेच्या निकालाच्या टक्केवारीचे वर्ग आणि त्या वर्गात असणारी विद्यार्थी संख्या खालील सारणीत दिली आहे. या सारणीवरून वारंवारता बहुभुज काढा. निकाल टक्के विद्यार्थी संख्या 30-40 7 40-50 33 50-60 45 60-70 65 70-80 47 80-90 18 90-100 5 The following table shows the classification of percentages of marks of students and the number of students. Draw a frequency polygon from the table. Result (Percentage) No. of Students 30-40 7 40-50 33 50-60 45 60-70 65 70-80 47 80-90 18 90-100 5$
Pictorial Representation of Statistical Data
Q5(ii) $खालील वृत्तालेखामध्ये शाळेच्या कॅप्टन पदासाठी स्पर्धा करणाऱ्या चार विद्यार्थ्यांना मिळालेल्या वैध मतांचे विवरण दिले आहे. वैध मतांची एकूण संख्या 720 आहे. तर पुढील प्रश्नांची उत्तरे द्या : (a) निवडणूक कोणी जिंकली ? (b) कमीत कमी मते किती ? ती कोणाला मिळाली ? (c) विजेत्याने सर्वात जवळच्या प्रतिस्पर्ध्याला किती मतांनी पराभूत केले ? The following pie diagram represents the number of valid votes obtained by four students; who contested for school captain. The total of valid votes polled was 720. Answer the following questions: (a) Who has won the election? (b) What is the minimum number of votes? Who got it? (c) By how many votes did the winner defeat the nearest contestant?$
Pictorial Representation of Statistical Data

March 2026

4 q

Q2(B)(v) $\sum x_i f_i = 1265$
Mean, Median and Mode of Grouped Data
Q3(B)(iv) $पुढील सामग्री आयतालेखाद्वारे दर्शवा : विद्यार्थ्यांची उंची (सेमी) विद्यार्थी संख्या 135-140 4 140-145 12 145-150 16 150-155 8 Draw a histogram of the following data: Height of Students (cm) No. of Students 135-140 4 140-145 12 145-150 16 150-155 8$
Pictorial Representation of Statistical Data
Q4(iii) $शाळेतील 105 विद्यार्थ्यांनी पूरग्रस्तांसाठी जमवलेल्या निधीची वारंवारता सारणी दिली आहे. त्यावरून जमा केलेल्या निधीचा मध्यक काढा : निधी (रुपये) विद्यार्थी संख्या 10-20 10 20-30 37 30-40 15 40-50 20 50-60 7 60-70 8 70-80 8 The following table shows the funds collected by 105 students for flood affected people. Find the median of the data. Fund (Rupees) No. of Students 10-20 10 20-30 37 30-40 15 40-50 20 50-60 7 60-70 8 70-80 8$
Mean, Median and Mode of Grouped Data
Q5(i) $a$
Pictorial Representation of Statistical Data

July 2025

5 q

Q1(B)(iv) $6-10 या वर्गाचा वर्गमध्य काढा. Find the class mark of the class 6-10.$
Mean, Median and Mode of Grouped Data

Q2(A)(iii)

\dfrac{40}{100} \times 360^\circ =

Pictorial Representation of Statistical Data

Q2(B)(v) $\sum f_i d_i = 10,000$
Mean, Median and Mode of Grouped Data
Q3(B)(i) $खालील सारणीत 210 कुटुंबांची वार्षिक गुंतवणूक दिली आहे. त्यावरून आयतालेख काढा : गुंतवणूक (हजार रुपयांमध्ये) कुटुंबांची संख्या 10-20 30 20-30 50 30-40 60 40-50 55 50-60 15 In the following table the yearly investment made by 210 families is given. From this information draw the histogram. Investment (Thousand Rupees) Number of families 10-20 30 20-30 50 30-40 60 40-50 55 50-60 15$
Pictorial Representation of Statistical Data
Q4(iii) $खालील वारंवारता वितरणामध्ये एका दवाखान्यातील 300 रुग्णांचे वय (वर्षांमध्ये) आणि रुग्णांची संख्या दिली आहे. त्यावरून रुग्णांच्या वयाचे मध्यक काढा : वय (वर्षांमध्ये) रुग्णांची संख्या 10-20 60 20-30 42 30-40 55 40-50 70 50-60 53 60-70 20 In the following frequency distribution table ages of 300 patients and number of patients in a hospital is given. Find the median age of the patients. Age (In years) Number of patients 10-20 60 20-30 42 30-40 55 40-50 70 50-60 53 60-70 20$
Mean, Median and Mode of Grouped Data

March 2025

4 q

Q2(B)(v)

(x_i)

Mean, Median and Mode of Grouped Data

Q3(B)(iv) $एका जनरल स्टोअरमधील विविध वस्तूंच्या किंमती व त्या वस्तूंची मागणी यांची वर्गीकृत वारंवारता सारणी दिली आहे. त्यावरून किंमतीचा मध्यक काढा. वस्तूंची किंमत (रुपये) वस्तूंची संख्या 20 पेक्षा कमी 140 20-40 100 40-60 80 60-80 60 80-100 20 In a general store the prices of different articles and its demand is shown in the following frequency distribution table. Find the Median of the prices. Price in Rupees No. of Articles Less than 20 140 20-40 100 40-60 80 60-80 60 80-100 20$
Mean, Median and Mode of Grouped Data
Q4(iii) $x$
Pictorial Representation of Statistical Data
Q5(ii) $एका रक्तगट तपासणी शिबिरामधील रक्तगटानुसार व्यक्तींची टक्केवारीमध्ये विभागणी खालील वृत्तालेखात दिली आहे. त्यावरून खालील प्रश्नांची उत्तरे लिहा : (a) प्रत्येक रक्तगटासाठी केंद्रीय कोनाचे माप काढा. (b) B या रक्तगटात 600 व्यक्ती असतील तर एकूण व्यक्तींची संख्या काढा. The following pie-diagram shows percentage of persons according to blood group in a blood group checking camp. Answer the following questions: (a) Find the measure of central angle for each blood group. (b) Find the total number of persons, if there are 600 persons of blood group B.$
Pictorial Representation of Statistical Data

July 2024

4 q

Q2(B)(v) $एका कुटुंबाच्या वार्षिक गुंतवणुकीचा वृत्तालेख खालील आकृतीत दिला आहे. त्यावरून खालील प्रश्नांची उत्तरे लिहा. (a) शेअर्समध्ये गुंतवलेली रक्कम 2,000 रुपये असल्यास एकूण गुंतवणूक किती ? (b) पोस्टातील गुंतवणूक किती ? The annual investments of a family are shown in the following pie diagram. Answer the following questions based on it. (a) If the investment in the shares is Rs. 2,000, find the total investment. (b) How much amount is invested in the Post?$
Pictorial Representation of Statistical Data
Q3(B)(iv) $एका महामार्गावरील टोलनाक्यावर सकाळी 6 ते संध्याकाळी 6 या वेळेत जमा होणारा कर (रुपयांत) व वाहन संख्या यांची वारंवारता सारणी दिली आहे. त्यावरून जमा होणाऱ्या कराचे ‘गृहीतमध्य’ पद्धतीने मध्य काढा : जमा कर (रुपये) वाहन संख्या 300-400 80 400-500 110 500-600 120 600-700 70 700-800 40 In the following table, the toll (in Rs.) paid from 6 am to 6 pm by drivers and the number of vehicles is shown. Find the mean of the toll by 'assumed mean' method. Toll (Rs.) No. of Vehicles 300-400 80 400-500 110 500-600 120 600-700 70 700-800 40$
Mean, Median and Mode of Grouped Data
Q4(iii) $10\%$
Mean, Median and Mode of Grouped Data
Q5(i) $पुढील सामग्री आयतालेखाद्वारे दर्शवा : विद्यार्थ्यांचा बुद्ध्यांक विद्यार्थी संख्या 60-80 4 80-100 12 100-120 16 120-140 8 Draw histogram of the following data: Students I.Q. Number of Students 60-80 4 80-100 12 100-120 16 120-140 8$
Pictorial Representation of Statistical Data

March 2024

4 q

Q2(B)(v) $खालील सारणीत एका सॉफ्टवेअर कंपनीतील दैनंदिन कामाचे तास व तेवढा वेळ काम करणाऱ्या कर्मचाऱ्यांची संख्या दिली आहे. त्यावरून ‘वरच्या वर्गमर्यादेपेक्षा कमी’ संचित वारंवारता वितरण सारणी तयार करा : दैनंदिन कामाचे तास कर्मचाऱ्यांची संख्या 8-10 150 10-12 500 12-14 300 14-16 50 The following table shows the classification of the number of workers and the number of hours they work in a software company. Prepare a 'less than' upper limit type cumulative frequency distribution table: Number of hours daily Number of workers 8-10 150 10-12 500 12-14 300 14-16 50$
Mean, Median and Mode of Grouped Data

Q3(A)(i)

खालील वारंवारता वितरण सारणीत एका पेट्रोलपंपावर पेट्रोल भरणाऱ्या वाहनांची संख्या आणि वाहनांमध्ये भरलेले पेट्रोल याची माहिती दिली आहे. त्यावरून वाहनात भरलेल्या पेट्रोलच्या आकारमानाचे बहुलक काढण्याची कृती पूर्ण करा : वर्ग (भरलेले पेट्रोल लीटरमधे) वारंवारता (वाहनांची संख्या) 0.5-3.5 33 3.5-6.5 40 6.5-9.5 27 9.5-12.5 18 12.5-15.5 12 The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. Complete the activity to find the mode of the volume of petrol filled. Class (Petrol filled in Liters) Frequency (Number of Vehicles) 0.5-3.5 33 3.5-6.5 40 6.5-9.5 27 9.5-12.5 18 12.5-15.5 12

Mean, Median and Mode of Grouped Data

Q4(ii) $एका परीक्षेच्या निकालाच्या टक्केवारीचे वर्ग आणि त्या वर्गात असणारी विद्यार्थी संख्या खालील सारणीत दिली आहे. या सारणीवरून आयतालेख न काढता वारंवारता बहुभुज काढा : निकाल (टक्के) विद्यार्थी संख्या 20-40 25 40-60 65 60-80 80 80-100 15 The following table shows the classification of the percentage of marks of students and the number of students. Draw the frequency polygon from the table without drawing a histogram: Result (Percentage) Number of Students 20-40 25 40-60 65 60-80 80 80-100 15$
Pictorial Representation of Statistical Data
Q5(i) $शाळेच्या प्रशासनाने एका वर्षी विविध खेळावर खर्च केलेली रक्कम वृत्तालेखात दाखवली आहे. जर फुटबॉलवर खर्च केलेली रक्कम 9,000 रुपये असेल, तर पुढील प्रश्नांची उत्तरे लिहा : (a) खेळावर एकूण किती रक्कम खर्च केली ? (b) क्रिकेटवर किती रक्कम खर्च केली ? In the given figure, the pie diagram represents the amount spent on different sports by a school administration in a year. If the money spent on football is ₹9,000, answer the following questions: (a) What is the total amount spent on sports? (b) What is the amount spent on cricket?$
Pictorial Representation of Statistical Data

March 2023

4 q

Q2(B)(v)

A = 300

Mean, Median and Mode of Grouped Data

Q3(B)(iv) $The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of the data: No. of Mangoes No. of Trees 50-100 33 100-150 30 150-200 90 200-250 80 250-300 17$
Mean, Median and Mode of Grouped Data
Q4(ii) $Show the following data by a frequency polygon: Electricity bill (₹) Families 200-400 240 400-600 300 600-800 450 800-1000 350 1000-1200 160$
Pictorial Representation of Statistical Data
Q5(ii) $A survey was conducted for 180 people in a city. 70 ate pizza, 60 ate burgers and 50 ate chips. Draw a pie diagram for the given information.$
Pictorial Representation of Statistical Data

March 2020

4 q

Q2(B)(v) $L = 10$
Mean, Median and Mode of Grouped Data

Q3(A)(i)

= \dfrac{\text{No. of persons}}{200} \times 360

Pictorial Representation of Statistical Data

Q3(B)(iii) $A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by the direct method: Milk Sold (litre) No. of Customers 1 - 2 17 2 - 3 13 3 - 4 10 4 - 5 7 5 - 6 3$
Mean, Median and Mode of Grouped Data
Q4(i) $\text{Rs.}$
Pictorial Representation of Statistical Data

March 2019

7 q

Q1(A)(i) $66, 98, 54, 92, 87, 63, 72$
Median of Ungrouped Data
Q3(A)(ii) $The following table shows the daily supply of electricity to different places in a town. To show the information by a pie diagram, find the measures of the central angles of the sectors. Places Supply of electricity (Thousand units) Roads 4 Factories 12 Shops 6 Houses 8 Total 30$
Pictorial Representation of Statistical Data
Q5(i) $180$
Pictorial Representation of Statistical Data

The following frequency distribution table shows the distances travelled by some rickshaws in a day. Observe the table and answer the following questions.

Class (Daily distance travelled in km)	Continuous Classes	Frequency (Number of rickshaws)	Cumulative Frequency (less than type)
60-64	59.5-64.5	10	10
65-69	64.5-69.5	34	44
70-74	69.5-74.5	58	102
75-79	74.5-79.5	82	184
80-84	79.5-84.5	10	194
85-89	84.5-89.5	6	200

Q6(ii)(i)

Which is the modal class? Why?

Mean, Median and Mode of Grouped Data

Q6(ii)(ii) $Which is the median class and why?$
Mean, Median and Mode of Grouped Data
Q6(ii)(iii) $Write the cumulative frequency (C.F.) of the class preceding the median class.$
Mean, Median and Mode of Grouped Data
Q6(ii)(iv) $(h)$
Mean, Median and Mode of Grouped Data

March 2018

4 q

Q2(vi) $For a certain frequency distribution mean is 72 and median is 78, find the mode.$
Mean, Median and Mode of Grouped Data
Q3(v) $The marks obtained by a student in an examination out of 100 are given below. The total marks obtained in various subjects are as follows. Represent the above data using a pie diagram. Subject Marks Marathi 80 English 80 Science 100 Mathematics 100 Total 360$
Pictorial Representation of Statistical Data
Q4(iii) $Frequency distribution of daily commission received by 100 salesmen is given below. Find the mean daily commission received by salesmen, by assumed mean method. Daily commission (in Rs.) No. of Salesmen 100 - 120 20 120 - 140 45 140 - 160 22 160 - 180 9 180 - 200 4$
Mean, Median and Mode of Grouped Data
Q5(iii) $Draw histogram and frequency polygon on the same graph paper for the following frequency distribution: Class Frequency 15 - 20 20 20 - 25 30 25 - 30 50 30 - 35 40 35 - 40 25 40 - 45 25$
Pictorial Representation of Statistical Data

March 2017

7 q

Q1(iv) $Find the class mark of the class 35-39.$
Mean, Median and Mode of Grouped Data
Q2(iv) $A = 1200$
Mean, Median and Mode of Grouped Data
Q3(iv) $The following is the frequency distribution of waiting time at an ATM centre; draw a histogram to represent the data: Waiting time (in seconds) Number of Customers 0 - 30 10 30 - 60 54 60 - 90 68 90 - 120 28 120 - 150 20$
Pictorial Representation of Statistical Data
Q4(ii) $The following is the distribution of the size of certain farms from a taluka (tehsil). Find the median size of farms. Size of Farms (in acres) Number of Farms 5 - 15 7 15 - 25 12 25 - 35 17 35 - 45 25 45 - 55 31 55 - 65 5 65 - 75 3$
Mean, Median and Mode of Grouped Data
The following pie diagram represents the sectorwise loan amount in crores of rupees distributed by a bank. In the pie diagram the Agriculture sector subtends a central angle of $120^\circ$ and the Dairy sector subtends a central angle of $40^\circ$ ; the remaining sector is Industry.
Q4(iii)(a) $If the dairy sector receives Rs 20 crores, then find the total loan disbursed.$
Pictorial Representation of Statistical Data
Q4(iii)(b) $Find the loan amount for the agriculture sector and also for the industrial sector.$
Pictorial Representation of Statistical Data
Q4(iii)(c) $How much additional amount did the industrial sector receive than the agriculture sector?$
Pictorial Representation of Statistical Data

March 2016

6 q

Q1(vi) $Find the class mark of the classes 20-30 and 30-40.$
Mean, Median and Mode of Grouped Data
Q2(v) $Below is the given frequency distribution of words in an essay. Find the mean number of words written. Number of Words Number of Candidates 600 - 800 8 800 - 1000 22 1000 - 1200 40 1200 - 1400 18 1400 - 1600 12$
Mean, Median and Mode of Grouped Data
Q2(vi) $Subjectwise marks obtained by a student in an examination are given below. Draw pie diagram. Subject Marks Marathi 85 Hindi 85 Science 90 Mathematics 100 Total 360$
Pictorial Representation of Statistical Data
Q3(iii) $The measurements (in mm) of the diameters of the head of the screws are given below. Calculate the mean diameter of the head of a screw by 'Assumed Mean Method'. Diameter (in mm) No. of Screws 33 - 35 10 36 - 38 19 39 - 41 23 42 - 44 21 45 - 47 27$
Mean, Median and Mode of Grouped Data
Q3(iv) $The marks scored by students in Mathematics in a certain Examination are given below. Draw histogram for the above data. Marks Scored Number of Students 0 - 20 3 20 - 40 8 40 - 60 19 60 - 80 18 80 - 100 6$
Pictorial Representation of Statistical Data
Q3(v) $Draw the frequency polygon for the following frequency distribution: Rainfall (in cm) No. of Years 20 - 25 2 25 - 30 5 30 - 35 8 35 - 40 12 40 - 45 10 45 - 50 7$
Pictorial Representation of Statistical 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 2 times: Mar 2026, Jun 2026
Q1(B)(iv) $\sum x_i f_i = 1265$
Question 2
Asked 2 times: Mar 2017*, Jul 2025 (* = numbers or wording changed that year)
Q2(B)(v) $\sum f_i d_i = 10,000$
Question 3
Asked 2 times: Mar 2019, Mar 2025
Q4(iii) $x$
Question 4
Asked 2 times: Mar 2016*, Mar 2018 (* = numbers or wording changed that year)
Q3(v) $The marks obtained by a student in an examination out of 100 are given below. The total marks obtained in various subjects are as follows. Represent the above data using a pie diagram. Subject Marks Marathi 80 English 80 Science 100 Mathematics 100 Total 360$
Question 5
This type asked 6 times: Mar 2016, Mar 2017, Mar 2020, Jul 2024, Jul 2025, Mar 2026. This one: Mar 2026
Q3(B)(iv) $पुढील सामग्री आयतालेखाद्वारे दर्शवा : विद्यार्थ्यांची उंची (सेमी) विद्यार्थी संख्या 135-140 4 140-145 12 145-150 16 150-155 8 Draw a histogram of the following data: Height of Students (cm) No. of Students 135-140 4 140-145 12 145-150 16 150-155 8$
Question 6
This type asked 5 times: Mar 2016, Mar 2018, Mar 2023, Mar 2024, Jun 2026. This one: Jun 2026
Q4(i) $एका परीक्षेच्या निकालाच्या टक्केवारीचे वर्ग आणि त्या वर्गात असणारी विद्यार्थी संख्या खालील सारणीत दिली आहे. या सारणीवरून वारंवारता बहुभुज काढा. निकाल टक्के विद्यार्थी संख्या 30-40 7 40-50 33 50-60 45 60-70 65 70-80 47 80-90 18 90-100 5 The following table shows the classification of percentages of marks of students and the number of students. Draw a frequency polygon from the table. Result (Percentage) No. of Students 30-40 7 40-50 33 50-60 45 60-70 65 70-80 47 80-90 18 90-100 5$
Question 7
This type asked 5 times: Mar 2017, Mar 2024, Jul 2024, Mar 2025, Jun 2026. This one: Jun 2026
Q5(ii) $खालील वृत्तालेखामध्ये शाळेच्या कॅप्टन पदासाठी स्पर्धा करणाऱ्या चार विद्यार्थ्यांना मिळालेल्या वैध मतांचे विवरण दिले आहे. वैध मतांची एकूण संख्या 720 आहे. तर पुढील प्रश्नांची उत्तरे द्या : (a) निवडणूक कोणी जिंकली ? (b) कमीत कमी मते किती ? ती कोणाला मिळाली ? (c) विजेत्याने सर्वात जवळच्या प्रतिस्पर्ध्याला किती मतांनी पराभूत केले ? The following pie diagram represents the number of valid votes obtained by four students; who contested for school captain. The total of valid votes polled was 720. Answer the following questions: (a) Who has won the election? (b) What is the minimum number of votes? Who got it? (c) By how many votes did the winner defeat the nearest contestant?$
Question 8
This type asked 5 times: Mar 2017, Mar 2023, Mar 2025, Jul 2025, Mar 2026. This one: Mar 2026
Q4(iii) $शाळेतील 105 विद्यार्थ्यांनी पूरग्रस्तांसाठी जमवलेल्या निधीची वारंवारता सारणी दिली आहे. त्यावरून जमा केलेल्या निधीचा मध्यक काढा : निधी (रुपये) विद्यार्थी संख्या 10-20 10 20-30 37 30-40 15 40-50 20 50-60 7 60-70 8 70-80 8 The following table shows the funds collected by 105 students for flood affected people. Find the median of the data. Fund (Rupees) No. of Students 10-20 10 20-30 37 30-40 15 40-50 20 50-60 7 60-70 8 70-80 8$
Question 9
This type asked 4 times: Mar 2019, Mar 2020, Jul 2025, Jun 2026. This one: Jun 2026
Q1(A)(iv) $40\%$
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Question 10
This type asked 4 times: Mar 2020, Mar 2024, Jul 2024, Jun 2026. This one: Jun 2026
Q3(B)(iii) $काही कुटुंबांचा मासिक वीजवापर पुढील वर्गीकृत वारंवारता सारणीत दिला आहे. त्यावरून वीजवापराचे बहुलक काढा. वीजवापर (यूनिटस्) कुटुंबाची संख्या 0-20 13 20-40 50 40-60 70 60-80 100 80-100 80 100-120 17 Electricity used by some families is shown in the following table. Find the mode of electricity used. Use of Electricity (Units) No. of Families 0-20 13 20-40 50 40-60 70 60-80 100 80-100 80 100-120 17$

निधी (रुपये)	विद्यार्थी संख्या
10–20	10
20–30	37
30–40	15
40–50	20
50–60	7
60–70	8
70–80	8

Fund (Rupees)	No. of Students
10–20	10
20–30	37
30–40	15
40–50	20
50–60	7
60–70	8
70–80	8

वाहनाचा प्रकार	विद्यार्थ्यांचे शेकडा प्रमाण
सायकल	35
बस	$a$
रेल्वे	$2a$
रिक्षा	20

Mode of Transport	Percentage of Students
Bicycle	35
Bus	$a$
Railway	$2a$
Rickshaw	20

विविध बाबीं	प्रतिशत खर्च	केंद्रीय कोनाचे माप
अन्न	40	$\dfrac{40}{100} \times 360^\circ =$ ____ $^\circ$
कपडे	20	$\dfrac{20}{100} \times 360^\circ =$ ____ $^\circ$
शिक्षण	30	$\dfrac{30}{100} \times 360^\circ =$ ____ $^\circ$
इतर खर्च	10	$\dfrac{10}{100} \times 360^\circ =$ ____ $^\circ$
एकूण	100	$360^\circ$

वस्तूंची किंमत (रुपये)	वस्तूंची संख्या
20 पेक्षा कमी	140
20–40	100
40–60	80
60–80	60
80–100	20

Class	Class mark $x_i$	$d_i = x_i - 300$	Frequency $f_i$	$f_i d_i$
200–240	220	-80	5	-400
240–280	260	-40	10	-400
280–320	300	0	15	0
320–360	340	40	12	480
360–400	380	80	8	640
Total			$\sum f_i = 50$	$\sum f_i d_i = 320$

Electricity bill (₹)	Families
200–400	240
400–600	300
600–800	450
800–1000	350
1000–1200	160

Age group (in years)	No. of Persons	Measure of central angle
20 - 25	80	$\frac{80}{200} \times 360$
25 - 30	60	$\frac{60}{200} \times 360$
30 - 35	35	$\frac{35}{200} \times 360 = 63^\circ$
35 - 40	25	$\frac{25}{200} \times 360$
Total	200

Number of Words	Number of Candidates
600 - 800	8
800 - 1000	22
1000 - 1200	40
1200 - 1400	18
1400 - 1600	12

Mean of grouped data - Direct method

Direct method

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Mean of grouped data - Assumed mean method

Assumed mean method

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Mean of grouped data - Step deviation method

Step deviation method

Solved Example

Practice set 6.1

Median of grouped data

Solved Example

Median from a cumulative frequency table

Solved Examples

Practice set 6.2

Mode of grouped data

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Practice set 6.3

Histogram

Practice set 6.4

Frequency polygon

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Practice set 6.5

Pie diagram

To read a Pie diagram

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Practice set 6.6

Miscellaneous Problems - 6

What the board has asked from this chapter

June 2026

March 2026

July 2025

March 2025

July 2024

March 2024

March 2023

March 2020

March 2019

March 2018

March 2017

March 2016

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10