Question

Find the standard deviation for the data from the previous example

Short answer

The standard deviation$s_x=3.5$

Step-by-step solution

Content Introduction

A standard deviation is a measure of data dispersion in proportion to the mean. Data are grouped around the mean when the standard deviation is low, while data are more spread out when the standard deviation is high.

Content Explanation

We are given the data as follow:

The first class, $0-2$, has a mid point that is$1$.

Let us calculate mean for the given data,

localid="1648896750882" $$\begin{gathered} {\mu }_x=\sum _{}x.p\left(x\right) \\ \overline{x}=6(1,6,....,2) \\ \overline{x}=7.58 \end{gathered}$$

Now calculate standard deviation,

localid="1648729908811" $$\begin{gathered} s=\sqrt{\frac{1}{n-1}\sum _{i=1}^n{(x_i-{\mu }_x)}^2} \\ s=\sqrt{\frac{1}{5}{(1-7.58)}^2+,.......+{(2-7.58)}^2} \\ s=3.5 \end{gathered}$$