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NCERT Class XI Mathematics - Statistics - Solutions

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Question : 19
Total: 34
Find the mean and variance for the following frequency distributions in Exercises 7 and 8.
Classes Frequencies
0 - 302
30 - 60 3
60 - 905
90 - 12010
120 - 150 3
150 - 180 5
180 - 210 2

Solution:  
ClassesMid values
xi		 fi ui =
xi−105
30
 fiui fiui2
0 - 30 15 2 - 3- 6 18
30 - 6045 3 - 2- 6 12
60 - 90 75 5 - 1- 5 5
90 - 120 10510 0 0 0
120 - 150 13531 33
150 - 180 165 52 10 20
180 - 210 95 2 3 618
30 2 76

Let assumed mean (A) = 105
Mean (
−
x
) = A +
Σfiui
N
 × h = 105 +
2
30
 × 30 = 107
Variance (σ2) =
h2
N2
[NΣfiui2−(Σfiui)2] =
900
900
 [30 × 76 - 4]
= [2280 - 4] = 2276
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