Test Index

AP ICET 2024 6th May 2024 Shift 1

Question : 196 of 200

Marks: +1, -0

2,4,6,8,10

Solution:

The formula for the standard deviation

\sigma

of a data set

x_1, x_2, \dots, x_n

is:

\sigma=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}(x_i-\mu)^2},

where

\mu

is the mean of the data set. First, find the mean:

\mu=\frac{2+4+6+8+10}{5}=6.

Now, calculate the variance:

\text{ Variance }=\frac{1}{5}((2-6)^2+(4-6)^2+(6-6)^2+(8-6)^2+(10-6)^2)=\frac{1}{5}(16+4+0+4+16)=\frac{40}{5}=8

The standard deviation is the square root of the variance:

\sigma=\sqrt{8}=2\sqrt{2}.

Quick Tip

To calculate the standard deviation, first find the mean, then calculate the variance

by averaging the squared differences from the mean, and finally take the square

root.

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