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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 \[tex]$5 per share, and have reported annual revenue between $[/tex]\[tex]$ 5$[/tex] million and [tex]$\$[/tex] 1[tex]$ billion. The table below shows the ages of the chief executive officers for the first 73 ranked firms.

\begin{tabular}{|c|c|c|}
\hline
Age & Frequency & Relative Frequency & Cumulative Relative Frequency \\
\hline
$[/tex]40-44[tex]$ & 4 & & \\
\hline
$[/tex]45-49[tex]$ & 3 & & \\
\hline
$[/tex]50-54$ & 15 & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To solve this question, we need to fill in the missing Relative Frequency and Cumulative Relative Frequency for the age groups of the chief executive officers in the given table. We are given the frequencies for each age group, which are 4, 3, and 15, for a total of 73 firms.

### Step 1: Calculate the Relative Frequency
Relative Frequency for each age group is calculated by dividing the frequency of that age group by the total number of firms.

For the age group 40-44,
[tex]\[ \text{Relative Frequency} = \frac{4}{73} = 0.0547945205479452 \][/tex]

For the age group 45-49,
[tex]\[ \text{Relative Frequency} = \frac{3}{73} = 0.0410958904109589 \][/tex]

For the age group 50-54 (assuming [tex]$5 n-51$[/tex] is a typo),
[tex]\[ \text{Relative Frequency} = \frac{15}{73} = 0.2054794520547945 \][/tex]

### Step 2: Calculate the Cumulative Relative Frequency
The Cumulative Relative Frequency is determined by adding the Relative Frequencies consecutively.

For the age group 40-44,
[tex]\[ \text{Cumulative Relative Frequency} = 0.0547945205479452 \][/tex]

For the age group 45-49, we add the Relative Frequency of 45-49 to the Cumulative Relative Frequency of the 40-44 age group,
[tex]\[ \text{Cumulative Relative Frequency} = 0.0547945205479452 + 0.0410958904109589 = 0.0958904109589041 \][/tex]

For the age group 50-54, we add the Relative Frequency of 50-54 to the Cumulative Relative Frequency of the 45-49 age group,
[tex]\[ \text{Cumulative Relative Frequency} = 0.0958904109589041 + 0.2054794520547945 = 0.3013698630136986 \][/tex]

### Completed Table
Let’s fill in the calculated values into the table:

[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Age} & \text{Frequency} & \text{Relative Frequency} & \text{Cumulative Relative Frequency} \\ \hline 40-44 & 4 & 0.054795 & 0.054795 \\ \hline 45-49 & 3 & 0.041096 & 0.095890 \\ \hline 50-54 & 15 & 0.205479 & 0.301370 \\ \hline \end{array} \][/tex]

By following these steps, we have successfully calculated and completed the table for the ages of the chief executive officers for the first 73 ranked firms.

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