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

The following table shows the distribution of 1000 students’ scores in an exam:

 Scores Total Frequency 1000 20– 30– 40– 50– 60– 70– 80– 90– 123 127 127 131 129 127 133 103

Draw the ascending cumulative frequency curve, then determine the number of students whose scores are less than 85.

• A830
• B764
• C897
• D118

### Example

The following table shows the distribution of 1000 students’ scores in an exam:

 Scores Total Frequency 1000 20– 30– 40– 50– 60– 70– 80– 90– 123 127 127 131 129 127 133 103

Draw the ascending cumulative frequency curve, then determine the number of students whose scores are less than 85.

### Solution

First form an ascending cumulative frequency table.

The upper boundaries of setsFrequency
less than 200
less than 30123
less than 40250
less than 50377
less than 60508
less than 70637
less than 80764
less than 90897
less than 100

Then use the table to draw an ascending cumulative frequency curve. Locate 85 along the -axis and find the related frequency.

So, the number of students whose scores are less than 85 is 830.

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