Statistics — Mathematics textbook solutions

13.4 Mean Deviation

19 q

Worked · 7

13.1 Eg.1 $Find the mean deviation about the mean for the following data: 6, 7, 10, 12, 13, 4, 8, 12$
13.1 Eg.2 $Find the mean deviation about the mean for the following data : 12, 3, 18, 17, 4, 9, 17, 19, 20, 15, 8, 17, 2, 3, 16, 11, 3, 1, 0, 5$
13.1 Eg.3 $Find the mean deviation about the median for the following data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.$
13.1 Eg.4 $x_i$
13.1 Eg.5 $x_i$
13.1 Eg.6 $Find the mean deviation about the mean for the following data. Marks obtained 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Number of students 23814832$
13.1 Eg.7 $Calculate the mean deviation about median for the following data : Class 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 67151642$

$x_i$	2	5	6	8	10	12
$f_i$	2	8	10	7	8	5

$x_i$	3	6	9	12	13	15	21	22
$f_i$	3	4	5	2	4	5	4	3

Marks obtained	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Number of students	2	3	8	14	8	3	2

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	6	7	15	16	4	2

Practice · 12

Ex 13.1 Q1 $Find the mean deviation about the mean for the data: 4, 7, 8, 9, 10, 12, 13, 17$
Ex 13.1 Q2 $Find the mean deviation about the mean for the data: 38, 70, 48, 40, 42, 55, 63, 46, 54, 44$
Ex 13.1 Q3 $Find the mean deviation about the median for the data: 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17$
Ex 13.1 Q4 $Find the mean deviation about the median for the data: 36, 72, 46, 42, 60, 45, 53, 46, 51, 49$
Ex 13.1 Q5 $x_i$
Ex 13.1 Q6 $x_i$
Ex 13.1 Q7 $x_i$
Ex 13.1 Q8 $x_i$
Ex 13.1 Q9 $Find the mean deviation about the mean for the following data: Income per day in ₹ 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 Number of persons 489107543$
Ex 13.1 Q10 $Find the mean deviation about the mean for the following data: Height in cms 95-105 105-115 115-125 125-135 135-145 145-155 Number of boys 91326301210$
Ex 13.1 Q11 $Find the mean deviation about median for the following data : Marks 0-10 10-20 20-30 30-40 40-50 50-60 Number of Girls 68141642$
Ex 13.1 Q12 $Calculate the mean deviation about median age for the age distribution of 100 persons given below: Age (in years) 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 Number 5612142612169 [Hint Convert the given data into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval]$

$x_i$	5	10	15	20	25
$f_i$	7	4	6	3	5

$x_i$	10	30	50	70	90
$f_i$	4	24	28	16	8

$x_i$	5	7	9	10	12	15
$f_i$	8	6	2	2	2	6

$x_i$	15	21	27	30	35
$f_i$	3	5	6	7	8

Income per day in ₹	0-100	100-200	200-300	300-400	400-500	500-600	600-700	700-800
Number of persons	4	8	9	10	7	5	4	3

Height in cms	95-105	105-115	115-125	125-135	135-145	145-155
Number of boys	9	13	26	30	12	10

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Number of Girls	6	8	14	16	4	2

Age (in years)	16-20	21-25	26-30	31-35	36-40	41-45	46-50	51-55
Number	5	6	12	14	26	12	16	9

15 q

Worked · 5

13.2 Eg.8 $Find the variance of the following data: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24$
13.2 Eg.9 $x_i$
13.2 Eg.10 $Calculate the mean, variance and standard deviation for the following distribution : Class 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Frequency 371215832$
13.2 Eg.11 $x_i$
13.2 Eg.12 $Calculate mean, variance and standard deviation for the following distribution. Classes 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Frequency 371215832$

$x_i$	4	8	11	17	20	24	32
$f_i$	3	5	9	5	4	3	1

Class	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	3	7	12	15	8	3	2

$x_i$	3	8	13	18	23
$f_i$	7	10	15	10	6

Classes	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	3	7	12	15	8	3	2

Practice · 10

Ex 13.2 Q1 $Find the mean and variance for the data: 6, 7, 10, 12, 13, 4, 8, 12$
Ex 13.2 Q2 $n$
Ex 13.2 Q3 $Find the mean and variance for the data: First 10 multiples of 3$
Ex 13.2 Q4 $x_i$
Ex 13.2 Q5 $x_i$
Ex 13.2 Q6 $x_i$
Ex 13.2 Q7 $Find the mean and variance for the following frequency distribution: Classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210 Frequencies 23510352$
Ex 13.2 Q8 $Find the mean and variance for the following frequency distribution: Classes 0-10 10-20 20-30 30-40 40-50 Frequencies 5815166$
Ex 13.2 Q9 $Find the mean, variance and standard deviation using short-cut method Height in cms 70-75 75-80 80-85 85-90 90-95 95-100 100-105 105-110 110-115 No. of children 3477159663$
Ex 13.2 Q10 $The diameters of circles (in mm) drawn in a design are given below: Diameters 33-36 37-40 41-44 45-48 49-52 No. of circles 1517212225 Calculate the standard deviation and mean diameter of the circles. [ Hint First make the data continuous by making the classes as 32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5 - 48.5, 48.5 - 52.5 and then proceed.]$

$x_i$	6	10	14	18	24	28	30
$f_i$	2	4	7	12	8	4	3

$x_i$	92	93	97	98	102	104	109
$f_i$	3	2	3	2	6	3	3

$x_i$	60	61	62	63	64	65	66	67	68
$f_i$	2	1	12	29	25	12	10	4	5

Classes	0-30	30-60	60-90	90-120	120-150	150-180	180-210
Frequencies	2	3	5	10	3	5	2

Classes	0-10	10-20	20-30	30-40	40-50
Frequencies	5	8	15	16	6

Height in cms	70-75	75-80	80-85	85-90	90-95	95-100	100-105	105-110	110-115
No. of children	3	4	7	7	15	9	6	6	3

Diameters	33-36	37-40	41-44	45-48	49-52
No. of circles	15	17	21	22	25

11 q

Worked · 4

Misc Eg.13 $The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations.$
Misc Eg.14 $The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.$
Misc Eg.15 $x_1, x_2, \ldots, x_n$
Misc Eg.16 $The mean and standard deviation of 100 observations were calculated as 40 and 5.1, respectively by a student who took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?$

Practice · 7

Misc Q1 $The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.$
Misc Q2 $The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.$
Misc Q3 $The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.$
Misc Q4 $\bar{x}$
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:
Misc Q5(i) $If wrong item is omitted.$
Misc Q5(ii) $If it is replaced by 12.$
Misc Q6 $The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.$