## NCERT Solutions for Class 11 Maths Chapter 15 – Statistics Ex 15.2

#### Question 1:

Find the mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12

6, 7, 10, 12, 13, 4, 8, 12
Mean,
The following table is obtained.
 xi 6 –3 9 7 –2 4 10 –1 1 12 3 9 13 4 16 4 –5 25 8 –1 1 12 3 9 74

#### Question 2:

Find the mean and variance for the first natural numbers

The mean of first n natural numbers is calculated as follows.

#### Question 3:

Find the mean and variance for the first 10 multiples of 3

The first 10 multiples of 3 are
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Here, number of observations, = 10
The following table is obtained.
 xi 3 –13.5 182.25 6 –10.5 110.25 9 –7.5 56.25 12 –4.5 20.25 15 –1.5 2.25 18 1.5 2.25 21 4.5 20.25 24 7.5 56.25 27 10.5 110.25 30 13.5 182.25 742.5

#### Question 4:

Find the mean and variance for the data
 xi 6 10 14 18 24 28 30 f i 2 4 7 12 8 4 3

The data is obtained in tabular form as follows.
 xi f i fixi 6 2 12 –13 169 338 10 4 40 –9 81 324 14 7 98 –5 25 175 18 12 216 –1 1 12 24 8 192 5 25 200 28 4 112 9 81 324 30 3 90 11 121 363 40 760 1736
Here, N = 40,

#### Question 5:

Find the mean and variance for the data
 xi 92 93 97 98 102 104 109 f i 3 2 3 2 6 3 3

The data is obtained in tabular form as follows.
 xi f i fixi 92 3 276 –8 64 192 93 2 186 –7 49 98 97 3 291 –3 9 27 98 2 196 –2 4 8 102 6 612 2 4 24 104 3 312 4 16 48 109 3 327 9 81 243 22 2200 640
Here, N = 22,

#### Question 6:

Find the mean and standard deviation using short-cut method.
 xi 60 61 62 63 64 65 66 67 68 fi 2 1 12 29 25 12 10 4 5

The data is obtained in tabular form as follows.
 xi fi yi2 fiyi fiyi2 60 2 –4 16 –8 32 61 1 –3 9 –3 9 62 12 –2 4 –24 48 63 29 –1 1 –29 29 64 25 0 0 0 0 65 12 1 1 12 12 66 10 2 4 20 40 67 4 3 9 12 36 68 5 4 16 20 80 100 220 0 286
Mean,

#### Question 7:

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 2 3 5 10 3 5 2

 Class Frequency fi Mid-point xi yi2 fiyi fiyi2 0-30 2 15 –3 9 –6 18 30-60 3 45 –2 4 –6 12 60-90 5 75 –1 1 –5 5 90-120 10 105 0 0 0 0 120-150 3 135 1 1 3 3 150-180 5 165 2 4 10 20 180-210 2 195 3 9 6 18 30 2 76
Mean,

#### Question 8:

Find the mean and variance for the following frequency distribution.
 Classes 0-10 10-20 20-30 30-40 40-50 Frequencies 5 8 15 16 6

 Class Frequency fi Mid-point xi yi2 fiyi fiyi2 0-10 5 5 –2 4 –10 20 10-20 8 15 –1 1 –8 8 20-30 15 25 0 0 0 0 30-40 16 35 1 1 16 16 40-50 6 45 2 4 12 24 50 10 68
Mean,

#### Question 9:

Find the mean, variance and standard deviation using short-cut method
 Height in cms No. of children 70-75 3 75-80 4 80-85 7 85-90 7 90-95 15 95-100 9 100-105 6 105-110 6 110-115 3

 Class Interval Frequency fi Mid-point xi yi2 fiyi fiyi2 70-75 3 72.5 –4 16 –12 48 75-80 4 77.5 –3 9 –12 36 80-85 7 82.5 –2 4 –14 28 85-90 7 87.5 –1 1 –7 7 90-95 15 92.5 0 0 0 0 95-100 9 97.5 1 1 9 9 100-105 6 102.5 2 4 12 24 105-110 6 107.5 3 9 18 54 110-115 3 112.5 4 16 12 48 60 6 254
Mean,

#### Question 10:

The diameters of circles (in mm) drawn in a design are given below:
 Diameters No. of children 33-36 15 37-40 17 41-44 21 45-48 22 49-52 25

 Class Interval Frequency fi Mid-point xi fi2 fiyi fiyi2 32.5-36.5 15 34.5 –2 4 –30 60 36.5-40.5 17 38.5 –1 1 –17 17 40.5-44.5 21 42.5 0 0 0 0 44.5-48.5 22 46.5 1 1 22 22 48.5-52.5 25 50.5 2 4 50 100 100 25 199
Here, N = 100, h = 4
Let the assumed mean, A, be 42.5.
Mean,

#### Question 1:

From the data given below state which group is more variable, A or B?
 Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Group A 9 17 32 33 40 10 9 Group B 10 20 30 25 43 15 7