Relative Frequency Distribution

by | Sep 11, 2023 | Accounting

 

Consider the following frequency distribution:
Interval Frequency
1,000 < x ≤ 1,100 22
1,100 < x ≤ 1,200 38
1,200 < x ≤ 1,300 44
1,300 < x ≤ 1,400 16

a.) Construct the relative frequency distribution. What proportion of the observations are more than 1,100 but no more than 1,200?
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b.) Construct the cumulative frequency distribution. How many of the observations are 1,300 or less?
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c.) Construct the cumulative relative frequency distribution. What proportion of the observations are 1,300 or less? More than 1,300?
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Sample Answer

Sample Answer

a) Relative Frequency Distribution:

Interval Frequency Relative Frequency 1,000 < x ≤ 1,100 22 22/120 = 0.1833 1,100 < x ≤ 1,200 38 38/120 = 0.3167 1,200 < x ≤ 1,300 44 44/120 = 0.3667 1,300 < x ≤ 1,400 16 16/120 = 0.1333

The proportion of observations that are more than 1,100 but no more than 1,200 is 0.3167.

b) Cumulative Frequency Distribution:

Interval Frequency Cumulative Frequency 1,000 < x ≤ 1,100 22 22 1,100 < x ≤ 1,200 38 22 + 38 = 60 1,200 < x ≤ 1,300 44 60 + 44 = 104 1,300 < x ≤ 1,400 16 104 + 16 = 120

There are 120 observations that are 1,300 or less.

c) Cumulative Relative Frequency Distribution:

Interval Frequency Cumulative Relative Frequency 1,000 < x ≤ 1,100 22 22/120 = 0.1833 1,100 < x ≤ 1,200 38 (22 + 38)/120 = 0.5 1,200 < x ≤ 1,300 44 (22 + 38 + 44)/120 = 0.8667 1,300 < x ≤ 1,400 16 (22 + 38 + 44 + 16)/120 = 1

The proportion of observations that are 1,300 or less is 0.8667. The proportion of observations that are more than 1,300 is 1 – 0.8667 = 0.1333.

 

 

 

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