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13.Statistics
normal
જો $\sum_{i=1}^{5}(x_i-10)=5$ અને $\sum_{i=1}^{5}(x_i-10)^2=5$ હોય તો અવલોકનો $2x_1 + 7, 2x_2 + 7, 2x_3 + 7, 2x_4 + 7$ અને $2x_5 + 7$ નો પ્રમાણિત વિચલન મેળવો
A
$8$
B
$16$
C
$4$
D
$2$
Solution
$\because \operatorname{var} .\left(2 \mathrm{x}_{\mathrm{i}}+7\right)=4 \operatorname{var}\left(\mathrm{x}_{\mathrm{i}}\right)=4\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}^{2}}{5}-\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}}{5}\right)^{2}\right)$
$=4\left(\frac{25}{5}-\left(\frac{5}{5}\right)^{2}\right)=4(5-1)=16$
$\therefore \mathrm{S} \mathrm{D}=\sqrt{16}=4$
Standard 11
Mathematics
