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NCERT Class XI Mathematics - Statistics - Solutions

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Question : 10 of 34
Marks: +1, -0
Height (in cms) Number of boys
95 – 105 9
105 – 115 13
115 – 125 26
125 – 135 30
135 – 145 12
145 – 155 10
Solution:  
Height(in cms) Mid values
xix_i		 fif_i fixif_i x_i ∣xi−125.3∣|x_i - 125.3| fi∣xi−12.5.3∣f_i |x_i-12.5.3|
95 - 105 100 9 900 25.3 227.7
105 - 115 110 13 1430 15.3 198.9
115 - 125 120 26 3120 5.3 137.8
125 - 135 130 30 3900 4.7 141
135 - 145 140 12 1680 14.7 176.4
145 - 155 150 10 1500 24.7 247
100 12530 1128.8
Mean (xˉ)(\bar{x}) = 1N∑i=1nfixi\frac{1}{N} \sum\limits_{i=1}^{n} f_i x_i = 1100\frac{1}{100} × 12530 = 125.3
Mean deviation about mean = (xˉ)(\bar{x}) = 1N∑i=1nfi∣xi−xˉ∣\frac{1}{N} \sum\limits_{i=1}^{n} f_i |x_i - \bar{x}| = 1100\frac{1}{100} × 1128.8 = 11.28
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