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NCERT Class XI Mathematics - Statistics - Solutions

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Question : 17 of 34
Marks: +1, -0
xix_i 92 93 97 98 102 104 109
fif_i 3 2 3 2 6 3 3
Solution:  
xix_i fif_i fixif_i x_i (xi−100)(x_i-100) (xi−100)2(x_i-100)^2 fi(xi−100)2f_i (x_i-100)^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
Mean (x−)\left(\overset{-}{x}\right) = 1N∑ni=1fixi\frac{1}{N} \sum\limits^{\underset{i=1}{n}} f_i x_i = 122\frac{1}{22} × 2200 = 100
Variance (σ2)(\sigma^2) = 1N∑ni=1fi(xi−x−)2\frac{1}{N} \sum\limits^{\underset{i=1}{n}} f_i \left(x_i - \overset{-}{x}\right)^2 = 122\frac{1}{22} × 640 = 29.09
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