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 $5 per share, and have reported annual revenue between $5 million and $1 billion. the table below shows the ages of the chief executive officers for the first 60 ranked firms. complete this table and use it to answer the next 10 questions.

age	40 - 44	45 - 49	50 - 54	55 - 59	60 - 64	65 - 69	70 - 74
relative frequency	a					b
cumulative relative frequency	c					d

Explanation:

Step1: Calculate total frequency

First, find the total number of data - points by summing up the frequencies. $3 + 11+13 + 16+10+6 + 1=60$.

Step2: Calculate relative frequencies

The relative frequency of a class is the frequency of the class divided by the total frequency.
For the $40 - 44$ age - group: $A=\frac{3}{60}=0.05$
For the $45 - 49$ age - group: $\frac{11}{60}\approx0.183$
For the $50 - 54$ age - group: $\frac{13}{60}\approx0.217$
For the $55 - 59$ age - group: $\frac{16}{60}\approx0.267$
For the $60 - 64$ age - group: $\frac{10}{60}\approx0.167$
For the $65 - 69$ age - group: $\frac{6}{60}=0.1$
For the $70 - 74$ age - group: $\frac{1}{60}\approx0.017$

Step3: Calculate cumulative relative frequencies

The cumulative relative frequency of a class is the sum of the relative frequencies of that class and all previous classes.
For the $40 - 44$ age - group: $C = 0.05$
For the $45 - 49$ age - group: $0.05+0.183 = 0.233$
For the $50 - 54$ age - group: $0.233+0.217 = 0.45$
For the $55 - 59$ age - group: $0.45+0.267 = 0.717$
For the $60 - 64$ age - group: $0.717+0.167 = 0.884$
For the $65 - 69$ age - group: $0.884 + 0.1=0.984$
For the $70 - 74$ age - group: $0.984+0.017 = 1$

Answer:

Age	Frequency	Relative Frequency	Cumulative Relative Frequency
$45 - 49$	$11$	$0.183$	$0.233$
$50 - 54$	$13$	$0.217$	$0.45$
$55 - 59$	$16$	$0.267$	$0.717$
$60 - 64$	$10$	$0.167$	$0.884$
$65 - 69$	$6$	$0.1$	$0.984$
$70 - 74$	$1$	$0.017$	$1$