Chapter 10.2, Problem 22CCR

To determine

To calculate:The mean, median and mode for the given set of data.

Answer to Problem 22CCR

Mean of the given set of data is $Mean=18$ .

Median of the given set of data is $Median=18$ .

Mode of the given set of data are $Mode=16,18\&20$ .

Explanation of Solution

Given information:the table below shows the ages of people in a play.

Age of people	No. of people
16	3
17	1
18	3
19	2
20	3
21	1

Formula used:

The Mean of a given set of values is the average of the given set of values.

  $Mean=\frac{\text{sum}\text{of}\text{values}}{\text{number}\text{of}\text{values}}$

The Median of a givenset of values is the middle value of the ordered set.

  $Median=\left\{\begin{array}{l}{\left(\frac{n+1}{2}\right)}^{th}\text{term,}\text{if}n\text{is}\text{odd}\\ \\ \frac{{\left(\frac{n}{2}\right)}^{th}\text{term}+{\left(\frac{n}{2}+1\right)}^{th}\text{term}}{2},\text{if}n\text{is}\text{even}\end{array}\right\}$ .

The Mode of a given set of values is the most frequently observed value of the ordered set.

Calculation:

From the given table

Age of people	No. of people
16	3
17	1
18	3
19	2
20	3
21	1

The Mean of the given set of data is

  $\begin{array}{c}Mean=\frac{\text{sum}\text{of}\text{values}}{\text{number}\text{of}\text{values}}=\frac{\left(16\times 3\right)+\left(17\times 1\right)+\left(18\times 3\right)+\left(19\times 2\right)+\left(20\times 3\right)+\left(21\times 1\right)}{\left(3+1+3+2+3+1\right)}\\ =\frac{48+17+54+38+60+21}{13}\\ Mean=18.3\approx 18\end{array}$

The Median of the given set of data is given by

  $\begin{array}{l}\text{First}\text{arrange}\text{the}\text{given}\text{set}\text{of}\text{values}\text{in}\text{ascending order}\\ \text{16,16,16,17,18,18,18,19,19,20,20,20,21}\\ \\ \text{Here}n=13(odd)\\ \\ Median\text{=}{\left(\frac{n+1}{2}\right)}^{th}\text{term}\\ Median\text{=}{\left(\frac{13+1}{2}\right)}^{th}\text{term}=7^{th}\text{term}\\ Median=18\end{array}$

The Mode of the given set of data is given by

  $\begin{array}{l}\text{First}\text{arrange}\text{the}\text{given}\text{set}\text{of}\text{values}\text{in}\text{ascending order}\\ \text{16,16,16,17,18,18,18,19,19,20,20,20,21}\\ \\ \text{Here}\text{the}\text{most}\text{frequently}\text{occuring}\text{values}\text{are}\\ 16\left(\text{occurs}\text{3}\text{times}\right)\\ 18\left(\text{occurs}\text{3}\text{times}\right)\\ 20\left(\text{occurs}\text{3}\text{times}\right)\\ \\ \text{Hence}\text{the}Mode=16,18\&20\end{array}$

Hence Mean of the given set of datais $Mean=18$ .

Median of the given set of data is $Median=18$ .

Mode of the given set of data are $Mode=16,18\&20$ .