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Question

Mathematics Question on Variance and Standard Deviation

The standard deviation of 9,16,23,30,37,44,519, 16, 23, 30, 37, 44, 51 is

A

7

B

9

C

12

D

14

Answer

14

Explanation

Solution

Now, mean of given observation is xˉ=9+16+23+30+37+44+517=2107=30\bar{x}=\frac{9+16+23+30+37+44+51}{7}=\frac{210}{7}=30 ∴\therefore Standard deviation =Σ(xi−x)27=\sqrt{\frac{\Sigma\left(x_{i}-x\right)^{2}}{7}} =(9−30)2+(16−30)2+(23−30)2+(30−30)2+(37−30)2+(44−30)2+(51−30)27=\sqrt{\frac{(9-30)^{2}+(16-30)^{2}+(23-30)^{2}+(30-30)^{2}}{+(37-30)^{2}+(44-30)^{2}+(51-30)^{2}}}{7} =(−21)2+(−14)2+(−7)2+(0)2+(7)2+(14)2+(21)27=\sqrt{\frac{(-21)^{2}+(-14)^{2}+(-7)^{2}+(0)^{2}+(7)^{2}+(14)^{2}+(21)^{2}}{7}} =441+196+49+49+196+4417=\sqrt{\frac{441+196+49+49+196+441}{7}} =13727=\sqrt{\frac{1372}{7}} =196=14=\sqrt{196}=14