CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 15 – Statistics Maths
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Question 6:
Find the mean and standard deviation using short-cut method.
x 60 61 62 63 64 65 66 67 68
i
f 2 1 12 29 25 12 10 4 5
i
Solution 6:
The data is obtained in tabular form as follows.
x
i
f
x
i
i
64
2
y fy
1
i i
f
i
1
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
9
i i
i
Mean, 1fy 0
x=A h=64+ 1 64 0 64
N 100
2 9 9
2 h 2 2
Variance, N f
2 iy
i
fiy
i
N
i1 i1
1
2
100 286 0
100
2.86
= 2.86 1.69
Standard deviation
fi
2
y 1
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
Solution 7:
Class Frequency
f
i
Mid-point x
i
xi
105
yi
30
2
y
i
fi
y
i
fi
2
y
i
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