Chapter 11.1, Problem 39E

(a)

To determine

To Find: The mean, median and mode of the student’s age.

Answer to Problem 39E

The value of the mean is 19 year and the median is 18 years.

Explanation of Solution

Given:

The given pie chart is shown in Figure 1

  

Figure 1

The number of students is 200.

Calculation:

Consider the age of the student is X then the table for the frequency distribution of age represented by pie chart.

Table 1

Age, x	Proportion p	Frequency $f=200p$	$fx$
18	0.35	70	1260
19	0.3	60	1140
20	0.14	28	560
21	0.2	40	840
37	0.01	2	74
Total	1	200	387.4

The mean is calculated as,

  $\begin{array}{c}\overline{x}=\frac{{\displaystyle \sum fx}}{{\displaystyle \sum f}}\\ =\frac{3874}{200}\\ =19.37\text{yrs}\end{array}$

Since, the data is 200 data value so median will be average of 100 th and 101 st then the median is,

  $\begin{array}{c}\overline{m}=\frac{19+19}{2}\\ =19\end{array}$

The value of the mean is 19 year and the median is 18 years.