Chapter 2.1, Problem 25E

a.

To determine

Construct a frequency bar graph.

Answer to Problem 25E

Output obtained from MINITAB software for the gender and age group is:

Explanation of Solution

Calculation:

The given information is a table representing the numbers of people in various gender and age categories who used a video game console.

Software procedure:

• Step by step procedure to draw the bar chart for gender and age group 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 Gender and Age Group.
• Click OK

Observation:

From the bar graph, it can be seen that Males 18-34 has the highest frequency.

b.

To determine

Construct a relative frequency distribution for the data.

Answer to Problem 25E

The relative frequency distribution for the data is:

Gender and Age Group	Relative Frequency
Males 2-11	0.139
Females 2-11	0.108
Males 12-17	0.102
Females 12-17	0.066
Males 18-34	0.172
Females 18-34	0.124
Males 35-49	0.111
Females 35-49	0.099
Males 50+	0.037
Females 50+	0.042

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,

$\begin{array}{c}\text{Relative}\text{Frequency}\text{for Africa}=\frac{13}{93.7}\\ =0.139\end{array}$

Similarly, the relative frequencies for the gender and age group are obtained below:

Gender and Age Group	Frequency	Relative Frequency
Males 2-11	13	$\frac{13}{93.7}=0.139$
Females 2-11	10.1	$\frac{10.1}{93.7}=0.108$
Males 12-17	9.6	$\frac{9.6}{93.7}=0.102$
Females 12-17	6.2	$\frac{6.2}{93.7}=0.066$
Males 18-34	16.1	$\frac{16.1}{93.7}=0.172$
Females 18-34	11.6	$\frac{11.6}{93.7}=0.124$
Males 35-49	10.4	$\frac{10.4}{93.7}=0.111$
Females 35-49	9.3	$\frac{9.3}{93.7}=0.099$
Males 50+	3.5	$\frac{3.5}{93.7}=0.037$
Females 50+	3.9	$\frac{3.9}{93.7}=0.042$
Total	93.7

c.

To determine

Construct a relative frequency bar graph for these data.

Answer to Problem 25E

Output obtained from MINITAB software for the gender and age group is:

Explanation of Solution

Software procedure:

• Step by step procedure to draw the Bar chart for gender and age group 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 Gender and Age Group.
• Click OK

Observation:

From the graph, it can be seen that most probable people in the various gender and age categories who used a video game console is Male 18-34 and the least probable people in the various gender and age categories who used a video game console is Male 50+.

d.

To determine

Construct a pie chart.

Answer to Problem 25E

Output obtained from MINITAB software for gender and age group is:

Explanation of Solution

Calculation:

Software procedure:

• Step by step procedure to draw the bar chart for gender and age group using MINITAB software.
• Choose Graph > Pie Chart.
• Choose Chart values from table.
• Under categorical variable, select Gender and Age Group.
• Under Summary variables, select Relative Frequency.
• Click OK.

Observation:

There is about 17.2% of the people in Male 18-34 and the 3.7% of the people in Male 50+.

e.

To determine

Identify whether the statement “More than half of video gamers are male” is true or false.

Answer to Problem 25E

The statement “More than half of video gamers are male” is true.

Explanation of Solution

From the pie chart, it can be seen that the percentage of male video gamers are $13+9.6+16.1+10.4+3.5=52.6\%$.

Hence, the statement “More than half of video gamers are male” is true.

Statistics Concept Introduction

Pie Chart:

It is a circle that divided into sectors one for each category.

g.

To determine

Identify whether the statement “More than 40% of video gamers are female” is true or false.

Answer to Problem 25E

The statement “More than 40% of video gamers are female” is true.

Explanation of Solution

From the pie chart, it can be seen that the and the percentage of female video gamers are $10.1+6.2+11.6+9.3+3.9=41.1\%$.

Hence, the statement “More than 40% of video gamers are female” is true.

Statistics Concept Introduction

Pie Chart:

It is a circle that divided into sectors one for each category.

h.

To determine

Find the proportion of video gamers who are 35 or over.

Answer to Problem 25E

The proportion of video gamers is 35 or over is 0.289.

Explanation of Solution

From the pie chart, it can be seen that the proportion of video gamers that are 35 or over aged are $11.1+9.9+3.7+4.2=28.9\%$.

Hence, the proportion of video gamers is 35 or over is 0.289.