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Mathematics Question on Variance and Standard Deviation

The standard deviation for the scores 1,2,3,4,5,61, 2, 3, 4, 5, 6 and 77 is 22. Then, the standard deviation of 12,23,34,45,56,6712, 23, 34, 45, 56, 67 and 7878 is

A

2

B

4

C

22

D

11

Answer

22

Explanation

Solution

Here, n=7,n=7, sum =315 Now, Mean =3157=45=\frac{315}{7}=45 ∴\therefore Standard deviation =(12−45)2+(23−45)2+(34−45)2 +(45−45)2+(56−45)2+(67−45)2 +(78−45)2 7=\sqrt{\frac{\begin{aligned} & {{(12-45)}^{2}}+{{(23-45)}^{2}}+{{(34-45)}^{2}} \\\ & +{{(45-45)}^{2}}+{{(56-45)}^{2}}+{{(67-45)}^{2}} \\\ & +{{(78-45)}^{2}} \\\ \end{aligned}}{7}} =(33)2+(22)2+(11)2+0 +(11)2+(22)2+(33)2 7=\sqrt{\frac{\begin{aligned} & {{(33)}^{2}}+{{(22)}^{2}}+{{(11)}^{2}}+0 \\\ & +{{(11)}^{2}}+{{(22)}^{2}}+{{(33)}^{2}} \\\ \end{aligned}}{7}} =2(1089+484+121)7=33887=\sqrt{\frac{2(1089+484+121)}{7}}=\sqrt{\frac{3388}{7}} =484=22=\sqrt{484}=22