Chapter 10, Problem 17SGR

To determine

To calculate the standard deviation

Answer to Problem 17SGR

Standard deviation is 1.02

Explanation of Solution

Given information:

The data for number of days B mows the lawn in a week are,

2, 4, 3, 5, 3

Formula used:

Mean is,

  $\overline{x}=\frac{{\displaystyle \sum x}}{n}$

Median is,

  $sd=\sqrt{\frac{{\displaystyle \sum {(x-\overline{x})}^2}}{n}}$

Calculation:

For mean, substituting the values,

  $\overline{x}=\frac{2+4+3+5+3}{5}$

So,

  $\overline{x}=\frac{17}{5}$

On solving,

  $\overline{x}=3.4$

Hence, mean is 3.4

For standard deviation, substituting the values,

  $sd=\sqrt{\frac{{(2-3.4)}^2+{(4-3.4)}^2+{(3-3.4)}^2+{(5-3.4)}^2+{(3-3.4)}^2}{5}}$

So,

  $sd=\sqrt{\frac{\text{1}\text{.96+0}\text{.36+0}\text{.16+2}\text{.56+0}\text{.16}}{5}}$

On solving,

  $sd=\sqrt{1.04}$

On solving,

  $sd=1.02$

Hence, standard deviation is 1.02