Chapter 10, Problem 10MCQ

To determine

To calculate the standard deviation

Answer to Problem 10MCQ

$2.22

Explanation of Solution

Given information:

The data of how much Indigo’s friends spend,

$10,$5,$3,$6,$7,$8

For mean,

  $\overline{x}=\frac{10+5+3+6+7+8}{6}$

So,

  $\overline{x}=\frac{39}{6}$

On solving,

  $\overline{x}=6.5$

Hence, mean is 6.5

Standard deviation formula is,

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

Substituting the values,

  $sd=\sqrt{\frac{{(10-6.5)}^2+{(5-6.5)}^2+{(3-6.5)}^2+{(6-6.5)}^2+{(7-6.5)}^2+{(8-6.5)}^2}{6}}$

On solving,

  $sd=\sqrt{\frac{\text{12}\text{.25+2}\text{.25+12}\text{.25+0}\text{.25+0}\text{.25+2}\text{.25}}{6}}$

So,

  $sd=\sqrt{\frac{29.5}{6}}$

On solving,

  $sd=2.22$

Hence, standard deviation is $2.22