Chapter 10, Problem 9MCQ

a.

To determine

To calculate the standard deviation

Answer to Problem 9MCQ

Standard deviation is 1.66

Explanation of Solution

Given information:

Data set of ages of children playing at the play area at the mall,

2, 3, 2, 2, 4, 2, 3, 2, 8, 3, 4, 2

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,

  $\overline{x}=\frac{2+3+2+2+4+2+3+2+8+3+4+2}{12}$

So,

  $\overline{x}=\frac{37}{12}$

On solving,

  $\overline{x}=3.08$

Hence mean is 3.08

For Standard deviation, substituting the values,

  $sd=\sqrt{\frac{\begin{array}{}$ {(2-3.08)}^2+{(3-3.08)}^2+{(2-3.08)}^2+{(2-3.08)}^2+{(4-3.08)}^2+{(2-3.08)}^2+{(3-3.08)}^2+$$ {(2-3.08)}^2+{(8-3.08)}^2+{(3-3.08)}^2+{(4-3.08)}^2+{(2-3.08)}^2$\end{array}}{12}}$

On solving,

  $sd=\sqrt{\frac{\begin{array}{}$ {(-1.08)}^2+{(-0.08)}^2+{(-1.08)}^2+{(-1.08)}^2+{(0.92)}^2+{(-1.08)}^2+{(-0.08)}^2+$$ {(-1.08)}^2+{(4.92)}^2+{(-0.08)}^2+{(0.92)}^2+{(-1.08)}^2$\end{array}}{12}}$

So,

  $sd=\frac{19.87}{12}$

On solving,

  $sd=1.66$

Hence, standard deviation is 1.66

Conclusion: standard deviation is 1.66

b.

To determine

To evaluate the mathematical practice.

Answer to Problem 9MCQ

Statistics.

Explanation of Solution

Given information:

Data set of ages of children playing at the play area at the mall,

2, 3, 2, 2, 4, 2, 3, 2, 8, 3, 4, 2

The mathematical practices used is statistics. Statistic includes mean, median, mode, standard deviation, quartiles,etc