Question

In Exercises 19 and 20, construct the relative frequency distributions and answer the given questions.

Blood Platelet Counts Construct one table (similar to Table 2-9 on page 47) that includes relative frequencies based on the frequency distributions from Exercises 7 and 8 and then compare them. Are there notable differences?

Short answer

The relative frequency distribution is constructed as follows:

Blood Platelet Count	Males	Females
0-99	0.7%
100-199	33.3%	17%
200-299	58.8%	62.6%
300-399	6.5%	19%
400-499	0%	0%
500-599	0%	1.4%
600-699	0.7%

Although absolutely no female has a blood platelet count less than 100 and above 600 as compared to men; overall, there is no major difference in the distribution of platelet counts for females and males.

Step-by-step solution

Given information

The grouped frequency distributions of the blood platelet count of males and females are provided.

Define relative frequency

The relative frequency of a class interval in a grouped frequency distribution is obtained using the given formula:

$\text{Relative}\text{frequency}\text{of}\text{a}\text{class}\text{interval}=\frac{\text{Frequency}\text{of}\text{a}\text{class}\text{interval}}{\text{Sum}\text{of}\text{all}\text{frequencies}}\times 100\%$

Construct the combined relative frequency table for blood platelet counts of males and females

A combined relative frequency distribution table is to be constructed for the given two frequency distributions of the blood platelet counts of males and females.

The table below shows the frequencies of theblood platelet count of males:

Blood Platelet Count of Males	Frequency
0-99	1
100-199	51
200-299	90
300-399	10
400-499	0
500-599	0
600-699	1

The sum of all frequencies is shown below:

$$\begin{gathered} \text{Sum}\text{of}\text{all}\text{frequencies}=1+51+90+10+0+0+1 \\ =153 \end{gathered}$$

Using the formula mentioned above, the relative frequencies for the different classes are calculated as shown below:

$$\begin{gathered} \text{Relative}{\text{freq}}_1=\frac{1}{153}\times 100\% \\ =0.7\% \\ \text{Relative}{\text{freq}}_2=\frac{51}{153}\times 100\% \\ =33.3\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_3=\frac{90}{153}\times 100\% \\ =58.8\% \\ \text{Relative}{\text{freq}}_4=\frac{10}{153}\times 100\% \\ =6.5\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_5=\frac{0}{153}\times 100\% \\ =0\% \\ \text{Relative}{\text{freq}}_6=\frac{0}{153}\times 100\% \\ =0\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_7=\frac{1}{153}\times 100\% \\ =0.7\% \end{gathered}$$

The table below shows the frequencies of the blood platelet count of females:

Blood Platelet Count of Females	Frequency
100-199	25
200-299	92
300-399	28
400-499	0
500-599	2

The sum of the frequencies is obtained below:

$$\begin{gathered} \text{Sum}\text{of}\text{all}\text{frequencies}=25+92+28+0+2 \\ =147 \end{gathered}$$

Using the formula mentioned above, the relative frequencies for the different classes are calculated as shown below:

$$\begin{gathered} \text{Relative}{\text{freq}}_1=\frac{25}{147}\times 100\% \\ =17\% \\ \text{Relative}{\text{freq}}_2=\frac{92}{147}\times 100\% \\ =62.6\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_3=\frac{28}{147}\times 100\% \\ =19\% \\ \text{Relative}{\text{freq}}_4=\frac{0}{147}\times 100\% \\ =0\% \end{gathered}$$

$$\begin{gathered} \text{Relative}{\text{freq}}_5=\frac{2}{147}\times 100\% \\ =1.4\% \end{gathered}$$

The combined relative frequency table is obtained as follows:

Blood Platelet Count	Males	Females
0-99	0.7%
100-199	33.3%	17%
200-299	58.8%	62.6%
300-399	6.5%	19%
400-499	0%	0%
500-599	0%	1.4%
600-699	0.7%
Total	100%	100%

Comparison

The majority of the males and females have a blood platelet count between 200 and 299.

Very few men have a blood platelet count lower than 100 and above 600, whereas no female has a blood platelet count lower than 100 and greater than 600.

The distributions for the blood platelet counts of males and females appear to be right skewed.

Overall, there are no major differences in the blood platelet count of males and females.