Question

Forbes magazine published data on the best small firms in $2012$. These were firms which had been publicly traded for at least a year, have a stock price of at least $\backslash (5$per share, and have reported annual revenue between $\backslash )5$million and $\$1$billion. Table $1.37$shows the ages of the chief executive officers for the first $60$ranked firms.

a. What is the frequency for CEO ages between 54 and 65?

b. What percentage of CEOs are 65 years or older?

c. What is the relative frequency of ages under 50?

d. What is the cumulative relative frequency for CEOs younger than 55?

e. Which graph shows the relative frequency and which shows the cumulative relative frequency?

Short answer

(a) Frequency of CEO between age $54\text{to}65\text{is26}$

(b) Parent of CEO that is $65$years or older is $11.67\%$

(c) Relative frequency of age under $50$years is $0.1833$

(b) Cumulative relative frequency of age under $5$years is $0.45$

(e) Graph A represents relative frequency and graph B represents cumulative frequency.

Step-by-step solution

Given information (part a)

The number of CEO in the age group $55\text{to}59\text{and}60\text{to64is16and10}$respectively.

Explanation (part a)

$$\begin{gathered} \text{Frequencybetweenage}54\text{and}65=16+10 \\ =26 \end{gathered}$$

Given information (part b)

The number of CEO in the age group $65$years and older is $6\text{and1}$

Explanation (part b)

$\text{PercentofCEO65yearsandolder}=\frac{numberofCEOwithage65yearsandolder}{totalnumberofCEOs}\times 100$

role="math" localid="1647604992747" $$\begin{gathered} \text{PercentofCEO}65\text{yearsandolder}=\frac{6+1}{60}\times 100 \\ =11.67\% \end{gathered}$$

Given information (part c)

The number of CEO in the age group $45\text{to49}$years is $11$and the total number of CEO is $60$

Explanation (part c)

$$\begin{gathered} \text{Relativefrequencyunderage}50=\frac{numberofCEOwithage45to49years}{totalnumberofCEOs} \\ \text{Relativefrequencyunderage}50=\frac{11}{60} \\ =0.1833 \end{gathered}$$

Given information (part d)

The number of CEO under the age of $55$years is $3,11\text{and13}$respectively and the total number of CEOs is$60$

Explanation (part d)

$$\begin{gathered} \text{Cumulativerelativefrequencyunderage}55=\frac{numberofCEOwithunderage55}{totalnumberofCEOs} \\ \text{Cumulativerelativefrequencyunderage}55=\frac{3+11+13}{60} \\ =0.45 \end{gathered}$$

Given information (part e)

Given the graph A - CEO's ages and graph B - Age

Explanation (part e)

A relative frequency graph will have the length of each bar equal to the relative frequency of each class interval, hence all the bars would be unequal and may or may not reflect any specific trend. but in the case of the cumulative frequency graph, since the cumulative frequency values go on increases as we move to further class intervals, the bar on the graph also goes on the increasing trend. thus graph A represents relative frequency data and graph B represents cumulative relative frequency data.