Chapter 14, Problem 22SGA

To determine

To find the standard deviation.

Answer to Problem 22SGA

  $1.74$

Explanation of Solution

Given:

A number cube is tossed $10$ times with the following results-

  $5,1,5,4,2,3,6,2,5,1$

Calculation:

Arranging the data in the ascending order as follows-

  $1,1,2,2,3,4,5,5,5,5,6$

First finding the mean as follows-

  $\begin{array}{l}=\frac{1+1+2+2+3+4+5+5+5+5+6}{10}\\ =3.4\end{array}$

Now, determine the standard deviation as follows-

  $\begin{array}{l}\sigma =\sqrt{{\left(2(1-3.4)\right)}^2+{\left(2(2-3.4)\right)}^2+{\left(3-3.4\right)}^2+{\left(4-3.4\right)}^2+{\left(4(5-3.4)\right)}^2+{\left(6-3.4\right)}^2}\\ \approx 1.74\end{array}$