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NCERT Class XI Mathematics - Statistics - Solutions

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Question : 24 of 34
Marks: +1, -0
From the prices of shares X and Y below, find out which is more stable in value :
X35 54 52 53 56 58 52 5051 49
Y108 107 105105106107104 103 104 101
Solution:  
X Y (X−X‾)(X-\overline{X}) (Y−Y‾)(Y-\overline{Y})(X−X‾)2(X-\overline{X})^2 (Y−Y‾)(Y-\overline{Y})
35108 - 16 3 2569
54 107 329 4
52105 1 01 0
53 10520 4 0
56 10651 25 1
58 107 72 49 4
52 1041 - 1 1 1
50 103 - 1 - 2 1 4
51 1040 − 1 0 1
49101 - 2 - 4 4 16
510 1050 350 40
X‾\overline{X} = 21010\frac{210}{10} = 51 , Y‾\overline{Y} = 105010\frac{1050}{10} = 105
σX\sigma_X = Σ(X−X‾)2n\sqrt{\frac{\Sigma (X-\overline{X})^2}{n}} = 35010\sqrt{\frac{350}{10}} = 5.92
σy\sigma_y = Σ(Y−Y‾)2n\sqrt{\frac{\Sigma (Y-\overline{Y})^2}{n}} = 4010\sqrt{\frac{40}{10}} = 2
C.V. of X = σXX\frac{\sigma_X}{X} × 100 = 5.9251\frac{5.92}{51} × 100 = 11.60
C.V. of Y = σYY\frac{\sigma_Y}{Y} × 100 = 2105\frac{2}{105} × 100 = 1.9
Since C.V. of Y < C.V. of X
Thus prices of share Y are more stable.
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