Chapter 10, Problem 18SGR

To determine

To calculate mean and standard deviation

Answer to Problem 18SGR

Mean is 33 and standard deviation is 15.23

Explanation of Solution

Given information:

The data of how much candy each team member sold,

20,25,30,50,40,60,20,10,42

Formula used:

Mean is,

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

Standard deviation is,

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

Calculation:

For mean, substituting the values,

  $\overline{x}=\frac{20+25+30+50+40+60+20+10+42}{9}$

So,

  $\overline{x}=\frac{297}{9}$

On solving,

  $\overline{x}=33$

Hence, mean is 33.

For standard deviation, substituting the values,

  $sd=\sqrt{\frac{\begin{array}{}$ {(20-33)}^2+{(25-33)}^2+{(30-33)}^2+{(50-33)}^2+{(40-33)}^2+{(60-33)}^2+{(20-33)}^2+{(10-33)}^2$$ +{(42-33)}^2$\end{array}}{9}}$

So,

  $sd=\sqrt{\frac{\text{169+64+9+289+49+729+169+529+81}}{9}}$

So,

  ${\sigma }_X=\sqrt{232}$

On solving,

  $\sigma =15.23$

Hence, standard deviation is 15.23