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Forzzy magazine published data on the best small firms last year. These were firms which had been publicly traded for at least a year, have a stock price of at least [tex][tex]$\$[/tex]5[tex]$[/tex] per share, and have reported annual revenue between [tex]$[/tex]\[tex]$5$[/tex][/tex] million and [tex][tex]$\$[/tex]1$[/tex] billion. The table below shows the ages of the chief executive officers for the first 96 ranked firms. Round the relative frequency to four decimal places.

Frequency Table
\begin{tabular}{|c|c|c|c|}
\hline
Age & Frequency & Relative Frequency & Cumulative Frequency \\
\hline
40-44 & 16 & & \\
\hline
45-49 & 17 & & \\
\hline
50-54 & 9 & & \\
\hline
55-59 & 17 & & \\
\hline
60-64 & 16 & & \\
\hline
65-69 & 12 & & \\
\hline
70-74 & 9 & & \\
\hline
Total & 96 & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To fill in the missing relative frequencies and cumulative frequencies in the given frequency table, let's follow each step methodically:

1. Calculate the Relative Frequencies:
[tex]\[ \text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Number of Firms}} \][/tex]
Given that the total number of firms is 96, we will use this number to calculate the relative frequency for each age group and round them to four decimal places.

- For Age 40-44:
[tex]\[ \text{Relative Frequency} = \frac{16}{96} = 0.1667 \][/tex]
- For Age 45-49:
[tex]\[ \text{Relative Frequency} = \frac{17}{96} = 0.1771 \][/tex]
- For Age 50-54:
[tex]\[ \text{Relative Frequency} = \frac{9}{96} = 0.0938 \][/tex]
- For Age 55-59:
[tex]\[ \text{Relative Frequency} = \frac{17}{96} = 0.1771 \][/tex]
- For Age 60-64:
[tex]\[ \text{Relative Frequency} = \frac{16}{96} = 0.1667 \][/tex]
- For Age 65-69:
[tex]\[ \text{Relative Frequency} = \frac{12}{96} = 0.1250 \][/tex]
- For Age 70-74:
[tex]\[ \text{Relative Frequency} = \frac{9}{96} = 0.0938 \][/tex]

2. Calculate the Cumulative Frequencies:
[tex]\[ \text{Cumulative Frequency} = \sum \text{Frequencies from previous groups} \][/tex]
- For Age 40-44:
[tex]\[ \text{Cumulative Frequency} = 16 \][/tex]
- For Age 45-49:
[tex]\[ \text{Cumulative Frequency} = 16 + 17 = 33 \][/tex]
- For Age 50-54:
[tex]\[ \text{Cumulative Frequency} = 33 + 9 = 42 \][/tex]
- For Age 55-59:
[tex]\[ \text{Cumulative Frequency} = 42 + 17 = 59 \][/tex]
- For Age 60-64:
[tex]\[ \text{Cumulative Frequency} = 59 + 16 = 75 \][/tex]
- For Age 65-69:
[tex]\[ \text{Cumulative Frequency} = 75 + 12 = 87 \][/tex]
- For Age 70-74:
[tex]\[ \text{Cumulative Frequency} = 87 + 9 = 96 \][/tex]

Now, updating the table with the calculated relative and cumulative frequencies:

\begin{tabular}{|c|c|c|c|}
\hline Age & Frequency & Relative Frequency & Cumulative Frequency \\
\hline [tex]$40-$[/tex]44 & 16 & 0.1667 & 16 \\
\hline [tex]$45-$[/tex]49 & 17 & 0.1771 & 33 \\
\hline [tex]$50-$[/tex]54 & 9 & 0.0938 & 42 \\
\hline [tex]$55-$[/tex]59 & 17 & 0.1771 & 59 \\
\hline [tex]$60-$[/tex]64 & 16 & 0.1667 & 75 \\
\hline [tex]$65-$[/tex]69 & 12 & 0.1250 & 87 \\
\hline [tex]$70-$[/tex]74 & 9 & 0.0938 & 96 \\
\hline Total & 96 & & \\
\hline
\end{tabular}

Thus, the table is now complete with the relative frequencies rounded to four decimal places and the cumulative frequencies calculated accurately.

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