Chapter 2, Problem 10RE

a.

To determine

Construct the frequency distribution with a class width of 5 and a lower limit of 45 for the first class.

Answer to Problem 10RE

The frequency distribution is,

Age	Frequency
45-49	2
50-54	1
55-59	4
60-64	6
65-69	6
70-74	6
75-79	4
80-84	3
85-89	2
90-94	4
Total	38

Explanation of Solution

Calculation:

The given information is that a data representing the age at which the all U.S. presidents died.

Frequency:

The frequencies are calculated by using the tally mark and the range of the data is from 45 to 94.

• Based on the given information, the class intervals are 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-79, 80-84, 85-89, 90-94.
• Make a tally mark for each value in the corresponding age class and continue for all values in the data.
• The number of tally marks in each class represents the frequency, f of that class.

Similarly, the frequency of remaining classes for the age is given below:

Age	Tally	Frequency
45-49	$\left|\right|$	2
50-54	$|$	1
55-59	$\left|\right|\left|\right|$	4
60-64	$\bcancel{\left|\right|\left|\right|}|$	6
65-69	$\bcancel{\left|\right|\left|\right|}|$	6
70-74	$\bcancel{\left|\right|\left|\right|}|$	6
75-79	$\left|\right|\left|\right|$	4
80-84	$\left|\right||$	3
85-89	$\left|\right|$	2
90-94	$\left|\right|\left|\right|$	4
Total		38

b.

To determine

Construct the frequency histogram based on the frequency distribution.

Answer to Problem 10RE

Output obtained from MINITAB software for the ages is:

Explanation of Solution

Calculation:

Frequency Histogram:

Software procedure:

• Step by step procedure to draw the frequency histogram for the ages using MINITAB software.
• Choose Graph > Bar Chart.
• From Bars represent, choose unique values from table.
• Choose Simple.
• Click OK.
• In Graph variables, enter the column of Frequency.
• In Categorical variables, enter the column of Ages.
• Click OK
• Select Edit Scale, Enter 0 in Gap between clusters.

Observation:

From the bar graph, it can be seen that maximum age at death for the U.S. presidents is in the interval 60-75.

c.

To determine

Construct a relative frequency distribution for the data.

Answer to Problem 10RE

The relative frequency distribution for the data is:

Age	Relative frequency
45-49	0.053
50-54	0.026
55-59	0.105
60-64	0.158
65-69	0.158
70-74	0.158
75-79	0.105
80-84	0.079
85-89	0.053
90-94	0.105

Explanation of Solution

Calculation:

Relative frequency:

The general formula for the relative frequency is,

$\text{Relative}\text{Frequency = }\frac{\text{Frequency}}{\text{Total frequency}}$

Therefore,

$\begin{array}{c}\text{Relative}\text{Frequency}\text{for the class 45-49}=\frac{2}{38}\\ =0.053\end{array}$

Similarly, the relative frequencies for the remaining ages are obtained below:

Age	Frequency	Relative frequency
45-49	2	$\frac{2}{38}=0.053$
50-54	1	$\frac{1}{38}=0.026$
55-59	4	$\frac{4}{38}=0.105$
60-64	6	$\frac{6}{38}=0.158$
65-69	6	$\frac{6}{38}=0.158$
70-74	6	$\frac{6}{38}=0.158$
75-79	4	$\frac{4}{38}=0.105$
80-84	3	$\frac{3}{38}=0.079$
85-89	2	$\frac{2}{38}=0.053$
90-94	4	$\frac{4}{38}=0.105$
Total	38

d.

To determine

Construct the relative frequency histogram based on the frequency distribution.

Answer to Problem 10RE

Output obtained from MINITAB software for the ages is:

Explanation of Solution

Calculation:

Relative Frequency Histogram:

Software procedure:

• Step by step procedure to draw the relative frequency histogram for the ages using MINITAB software.
• Choose Graph > Bar Chart.
• From Bars represent, choose unique values from table.
• Choose Simple.
• Click OK.
• In Graph variables, enter the column of Relative Frequency.
• In Categorical variables, enter the column of Ages.
• Click OK
• Select Edit Scale, Enter 0 in Gap between clusters.

Observation:

From the bar graph, it can be seen that maximum age at death for the U.S. presidents is in the interval 60-75.