# 8.3.2. Ascending and Descending Cumulative Frequency Tables and Their Graphical Representation

The years of experience of 100 workers in a factory ranges from 5 to 35 years. The table below shows the descending cumulative frequency distribution for the workers according to the years of experience. Fill in the frequency table below.

 Lower Boundaries of Sets Descending Cumulative Frequency 5 and more 10 and more 15 and more 20 and more 25 and more 30 and more 35 and more 100 89 77 61 42 28 0
 Years Frequency 5– 10– 15– 20– 25– 30– Total
• A11, 12, 16, 19, 14, 28, 100
• B23,12, 16, 19, 14, 28, 112
• C11, 28, 16, 19, 14, 28, 116
• D100, 89,77, 61, 42, 28, 397

### Example

The years of experience of 100 workers in a factory ranges from 5 to 35 years. The table below shows the descending cumulative frequency distribution for the workers according to the years of experience. Fill in the frequency table below.

 Lower Boundaries of Sets Descending Cumulative Frequency 5 and more 10 and more 15 and more 20 and more 25 and more 30 and more 35 and more 100 89 77 61 42 28 0
 Years Frequency 5– 10– 15– 20– 25– 30– Total

### Solution

To find the frequency for each set of years, find the difference between the corresponding cumulative frequency and the cumulative frequency that follows. For example, to find the frequency for the set , subtract the cumulative frequency for 10 and more from the cumulative frequency for 5 and more.

• Total frequency for 5 and more 100
• Frequency for set
• Frequency for set
• Frequency for set
• Frequency for set
• Frequency for set
• Frequency for set frequency for 30 and more 28.

Use the data to complete the frequency table.

 Years Frequency Total 11 12 16 19 14 28 100
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