Statistics – Exercise 15.2 – Class XI

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

Solution:

Given data is 6, 7, 10, 12, 13, 4, 8, 12

Statistics – Exercise 15.2 – Class XI

xi(xi –  x)(xi –  x)2
6-39
7-24
10-11
1239
13416
4-525
8-11
1239
74

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


  1. Find the mean and variance for the first n natural numbers

Solution:

Statistics – Exercise 15.2 – Class XI


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

Solution:

The first 10 multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Here, number of observations, n = 10

Statistics – Exercise 15.2 – Class XI

xi(xi – Mean.)(xi-Mean.)2
3-13.5182.25
6-10.5110.25
9-7.556.25
12-4.520.25
15-1.52.25
181.52.25
214.520.25
247.556.25
2710.5110.25
3013.5182.25
742.5

Statistics – Exercise 15.2 – Class XI


  1. Find the mean and variance for the data:
xi6101418242830
fi24712843

Solution:

xififixixi-mean(xi – mean)2fi(xi-Mean.)2
6212-13169338
10440-981324
14798-525175
1812216-1112
248192525200
284112981324
3039011121363
407601736

N=40

Statistics – Exercise 15.2 – Class XI

  1. Find the mean and variance for the data:
xi92939798102104109
fi3232633

Solution:

xififixixi-mean(xi – mean)2fi(xi-Mean.)2
               923276-864192
932186-74998
973291-3927
982196-248
10266122424
104331241648
1093327981243
222200640

N=22

Statistics – Exercise 15.2 – Class XI


  1. Find the mean and standard deviation for the data:
xi606162636465666768
fi21122925121045

Solution:

xififi=(xi-64)/Iyi2fiyifiyi2
602-416-832
611-39-39
6212-24-2448
6329-11-2929
64250000
6512111212
6610242040
674391236
6854162080
1002200286

N=100

Statistics – Exercise 15.2 – Class XI


  1. Find the mean and standard deviation for the data:
classes0-3030-6060-9090-120120-150150-180180-210
Frequencies23510352

Solution:

Classfrequencymidpoint xiyi=(xi-105)/30yi2fiyifiyi2
0-30215-39-618
30-60345-24-612
60-90575-11-55
90-120101050000
120-15031351133
150-1805165241020
180-210219539618
30276

N=30

7.png


  1. Find the mean and variance for the data:
Classes0-1010-2020-3030-4040-50
frequency5815166

Solution:

Classfrequencymidpoint xiyi=(xi-105)/30yi2fiyifiyi2
0-1055-24-1020
10-20815-11-88
20-3015250000
30-401635111616
40-50645241224
501068

N=50

Statistics – Exercise 15.2 – Class XI


  1. Find the mean, variance and standard deviation using the short cut method
Height in cmsNo. of children
70-753
75-804
80-857
85-907
90-9515
95-1009
100-1056
105-1106
110-1153

Solution:

Height in cmsNo. of childrenMidpoint xiyi = (xi-92.5)/5yi2fiyifiyi2
70-75372.5-416-1248
75-80477.5-39-1236
80-85782.5-24-1428
85-90787.5-11-77
90-951592.50000
95-100997.51199
100-1056102.5241224
105-1106107.5391854
110-1153112.54161248
606254

9.png


  1. The diameters of circles(in mm) drawn in a design are given below:
DiametersNo. of children
33-3615
37-4017
41-4421
45-4822
49-5225

Solution:

DiametersNo. of childrenMidpoint xiyi = (xi-92.5)/5yi2fiyifiyi2
33-361534.5-24-3060
37-401738.5-11-1717
41-442142.50000
45-482246.5112222
49-522550.52450100
10025199

10.png