Chapter 2.1, Problem 25E

Ages of video garners: The Nielsen Company estimated the numbers of people in various gender and age categories who used a video game console. The results are presented in the following frequency distribution.

1. Construct a frequency bar graph.
2. Construct a relative frequency distribution.
3. Construct a relative frequency bar graph.
4. Construct a pie chart.
5. True or false: More than half of video garners are male.
6. True or false: More than 40% of video garners are female.
7. What proportion of video garners are 35 or over?

To determine

To construct: A frequency bar graph.

Explanation of Solution

Given information: The Nielson Company estimated the numbers of people in various gender and age categories who used a video game console. The results are presented in the following frequency distribution.

Gender and age group	Frequency (in millions)
Males 2-11	13.0
Females 2-11	10.1
Males 12-17	9.6
Females 12-17	6.2
Males 18-34	16.1
Females 18-34	11.6
Males 35-49	10.4
Females 35-49	9.3
Males 50+	3.5
Females 50+	3.9

Solution:

From the given table, the frequency bar graph is given by

  

To determine

To construct: The relative frequency distribution.

Explanation of Solution

Given information:The Nielson Company estimated the numbers of people in various gender and age categories who used a video game console. The results are presented in the following frequency distribution.

Gender and age group	Frequency (in millions)
Males 2-11	13.0
Females 2-11	10.1
Males 12-17	9.6
Females 12-17	6.2
Males 18-34	16.1
Females 18-34	11.6
Males 35-49	10.4
Females 35-49	9.3
Males 50+	3.5
Females 50+	3.9

 Relative frequency=Frequency

  $Relativefrequency=\frac{Frequency}{ Sum\text{ of all }Frequency}$

Calculation:

From the given table,

The sum of all frequency is $13.0+10.1+9.6+6.2+16.1+11.6+10.4+9.3+3.5+3.9=93.7$

The table of relative frequency is given by

Gender and age group	Frequency (in millions)	Relative frequency
Males 2-11	13.0	$\frac{13.0}{93.7}=0.139$
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	$\frac{3.9}{93.7}=0.042$

To determine

To construct: A relative frequency bar graph.

Explanation of Solution

Given information:The Nielson Company estimated the numbers of people in various gender and age categories who used a video game console. The results are presented in the following frequency distribution.

Gender and age group	Frequency (in millions)
Males 2-11	13.0
Females 2-11	10.1
Males 12-17	9.6
Females 12-17	6.2
Males 18-34	16.1
Females 18-34	11.6
Males 35-49	10.4
Females 35-49	9.3
Males 50+	3.5
Females 50+	3.9

Definition used:

Histogram based on relative frequency is called relative frequency histogram.

Solution:

The Nielson Company estimated the numbers of people in various gender and age categories who used a video game console. The results are presented in the following frequency distribution.

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

From the above table, the relative frequency bar graph is given by

  

To determine

To construct: A pie chart

Explanation of Solution

Given information: The Nielson Company estimated the numbers of people in various gender and age categories who used a video game console. The results are presented in the following frequency distribution.

Gender and age group	Frequency (in millions)
Males 2-11	13.0
Females 2-11	10.1
Males 12-17	9.6
Females 12-17	6.2
Males 18-34	16.1
Females 18-34	11.6
Males 35-49	10.4
Females 35-49	9.3
Males 50+	3.5
Females 50+	3.9

Solution:

From the given table, the percentage of each gender and age group is given by

Gender and age group	Relative Frequency	Percentage
Males 2-11	0.139	13.9%
Females 2-11	0.108	10.8%
Males 12-17	0.102	10.2%
Females 12-17	0.066	6.6%
Males 18-34	0.172	17.2%
Females 18-34	0.124	12.4%
Males 35-49	0.111	11.1%
Females 35-49	0.099	9.9%
Males 50+	0.037	3.7%
Females 50+	0.042	4.2%

From the above table, the pie chart is given by

  

To determine

True or False: More than half of video gamers are male.

Answer to Problem 25E

True.

Explanation of Solution

Given information:The Nielson Company estimated the numbers of people in various gender and age categories who used a video game console. The results are presented in the following frequency distribution.

Gender and age group	Frequency (in millions)
Males 2-11	13.0
Females 2-11	10.1
Males 12-17	9.6
Females 12-17	6.2
Males 18-34	16.1
Females 18-34	11.6
Males 35-49	10.4
Females 35-49	9.3
Males 50+	3.5
Females 50+	3.9

Solution:

The sum of all frequency is $13.0+10.1+9.6+6.2+16.1+11.6+10.4+9.3+3.5+3.9=93.7$

The half of the frequency is 46.85.

The sum of total of male video gamer’s frequency is $13.0+9.6+16.1+10.4+3.5=52.6$ which is more than half of total frequency.

Therefore, it is true that more than half of video gamers are male.

To determine

True or False: More than 40% of video gamers are female.

Answer to Problem 25E

True.

Explanation of Solution

Given information:The Nielson Company estimated the numbers of people in various gender and age categories who used a video game console. The results are presented in the following frequency distribution.

Gender and age group	Frequency (in millions)
Males 2-11	13.0
Females 2-11	10.1
Males 12-17	9.6
Females 12-17	6.2
Males 18-34	16.1
Females 18-34	11.6
Males 35-49	10.4
Females 35-49	9.3
Males 50+	3.5
Females 50+	3.9

Solution:

The sum of all frequency is $13.0+10.1+9.6+6.2+16.1+11.6+10.4+9.3+3.5+3.9=93.7$

40% of the total frequency is $93.7\times \frac{40}{100}=37.48$

The sum of total of female video gamer’s frequency is $10.1+6.2+11.6+9.3+3.9=41.1$ which is more than 40% of total frequency.

Therefore, it is true that more than 40% of video gamers are female.

To determine

To find: The proportion of video gamers is 35 or over.

Answer to Problem 25E

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

Explanation of Solution

Given information:The Nielson Company estimated the numbers of people in various gender and age categories who used a video game console. The results are presented in the following frequency distribution.

Gender and age group	Frequency (in millions)
Males 2-11	13.0
Females 2-11	10.1
Males 12-17	9.6
Females 12-17	6.2
Males 18-34	16.1
Females 18-34	11.6
Males 35-49	10.4
Females 35-49	9.3
Males 50+	3.5
Females 50+	3.9

Solution:

The sum of all frequency is $13.0+10.1+9.6+6.2+16.1+11.6+10.4+9.3+3.5+3.9=93.7$

The sum of all frequency for which the video gamer is 35 or more is $10.4+9.3+3.5+3.9=27.1$

The proportion of video gamers is 35 or over is given by

  $\frac{27.1}{93.7}=0.289$

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