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.

(b)

To determine

To Find: The outliers and then find the outliers affect the mean, median and the mode.

Answer to Problem 39E

The age 37 years is the outlier as it is far away from the other observations so the mean pull upwards and the median is unaffected.

Explanation of Solution

Calculation:

Since, the age 37 years is the outlier as it is far away from the other observations so the mean pull upwards and the median is unaffected.

(c)

To determine

To Find: The diagram for the new circle graph that shows the distribution of the ages of this class and the find the mean, median and the mode of the students ages.

Answer to Problem 39E

The updated pie chart is shown in Figure 2

Explanation of Solution

Calculation:

Consider that after one year the age is increased by 1 so the mean is 20.37 years and the median is 20 years and the mode is 18 years.

The updated pie chart is shown in Figure 2

  

Figure 2