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 -3 9
7 -2 4
10 -1 1
12 3 9
13 4 16
4 -5 25
8 -1 1
12 3 9
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 -13.5 182.25
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

Statistics – Exercise 15.2 – Class XI


  1. Find the mean and variance for the data:
xi 6 10 14 18 24 28 30
fi 2 4 7 12 8 4 3

Solution:

xi fi fixi xi-mean (xi – mean)2 fi(xi-Mean.)2
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

N=40

Statistics – Exercise 15.2 – Class XI

  1. Find the mean and variance for the data:
xi 92 93 97 98 102 104 109
fi 3 2 3 2 6 3 3

Solution:

xi fi fixi xi-mean (xi – mean)2 fi(xi-Mean.)2
               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

N=22

Statistics – Exercise 15.2 – Class XI


  1. Find the mean and standard deviation for the data:
xi 60 61 62 63 64 65 66 67 68
fi 2 1 12 29 25 12 10 4 5

Solution:

xi fi fi=(xi-64)/I 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

N=100

Statistics – Exercise 15.2 – Class XI


  1. Find the mean and standard deviation for the data:
classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210
Frequencies 2 3 5 10 3 5 2

Solution:

Class frequency midpoint xi yi=(xi-105)/30 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

N=30

7.png


  1. Find the mean and variance for the data:
Classes 0-10 10-20 20-30 30-40 40-50
frequency 5 8 15 16 6

Solution:

Class frequency midpoint xi yi=(xi-105)/30 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

N=50

Statistics – Exercise 15.2 – Class XI


  1. Find the mean, variance and standard deviation using the 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

Solution:

Height in cms No. of children Midpoint xi yi = (xi-92.5)/5 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

9.png


  1. 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

Solution:

Diameters No. of children Midpoint xi yi = (xi-92.5)/5 yi2 fiyi fiyi2
33-36 15 34.5 -2 4 -30 60
37-40 17 38.5 -1 1 -17 17
41-44 21 42.5 0 0 0 0
45-48 22 46.5 1 1 22 22
49-52 25 50.5 2 4 50 100
100 25 199

10.png


 

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