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NCERT Class XI Mathematics - Statistics - Solutions

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Question : 20
Total: 34
Classes 0 - 1010 - 2020 - 30 30 - 40 40 - 50
Frequencies 58 15 16 6

Solution:  
Classes Mid values
xi		 fi ui =
xi−25
10
 fiui fiui2
0 - 10 5 5 - 2 - 10 20
10 - 20 15 8 - 1 - 8 8
20 - 30 25 15 0 0 0
30 - 40 35 16 1 16 16
40 - 50 45 6 2 12 24
50 10 68

Let assumed mean (A) = 25
Mean (
−
x
) = A +
Σfiui
N
 × h = 25 +
10
50
 × 10 = 25 + 2 = 27
Variance (σ2) =
h2
N2
[NΣfiui2−(Σfiui)2] =
(10)2
(50)2
 [50×68−(10)2]
=
100
2500
 [3400 - 100] =
1
25
 × 3300 = 132
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