Question

A magazine published data on the best small firms in a certain year. 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 68 ranked firms.

Age	Frequency	Relative Frequency	Cumulative Relative Frequency
40-44	9
45-49	11
50-54	13
55-59	16
60-64	10
65-69	8
70-74	1

(a) What is the frequency for CEO ages between (but not including) 54 and 65? (Enter your answer as a whole number.)


(b) What percentage of CEOs are 65 years or older? (Round your answer to the nearest whole number.)
%

(c) What is the relative frequency of ages under 50? (Round your answer to two decimal places.)


(d) What is the cumulative relative frequency for CEOs younger than 55? (Round your answer to two decimal places.)

Answer 1

Solution:

To find relative frequency , first find total of frequency column , then divide each frequency by total frequency.

To get cumulative relative frequency, add relative frequency from top to bottom.

Age	Frequency	Relative Frequency	Calculations	Cumulative Relative Frequency
40-44	9	0.13	0.13	0.13
45-49	11	0.16	=0.13+0.16=0.29	0.29
50-54	13	0.19	=0.29+0.19=0.49	0.49
55-59	16	0.24	=0.49+0.24=0.72	0.72
60-64	10	0.15	=0.72+0.15=0.87	0.87
65-69	8	0.12	=0.87+0.12=0.99	0.99
70-74	1	0.01	=0.99+0.01=1.00	1.00
	68

Part a) What is the frequency for CEO ages between (but not including) 54 and 65?

Frequency for CEO ages between (but not including) 54 and 65 = Frequency between 55-59 + Frequency between 60-64

Frequency for CEO ages between (but not including) 54 and 65 = 16+10

Frequency for CEO ages between (but not including) 54 and 65 = 26

Part b) What percentage of CEOs are 65 years or older?

Percentage of CEOs are 65 years or older = ( Relative frequency of 65-69 + Relative frequency of 70-74)*100

Percentage of CEOs are 65 years or older = ( 0.12 + 0.01) * 100

Percentage of CEOs are 65 years or older = 0.13 *100

Percentage of CEOs are 65 years or older = 13%

Part c) What is the relative frequency of ages under 50?

the relative frequency of ages under 50 = relative frequency of ages between( (40-44) + (45-49) )

the relative frequency of ages under 50 = 0.13 + 0.16

the relative frequency of ages under 50 = 0.29

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

the cumulative relative frequency for CEOs younger than 55 = the cumulative relative frequency for CEOs below 55

the cumulative relative frequency for CEOs younger than 55 = 0.13+0.16+0.19

the cumulative relative frequency for CEOs younger than 55 = 0.49