# 8.3.3. Arithmetic Mean, Median, and Mode

The following table shows the frequency distribution for the scores of 60 students in an exam:

 Sets Total Frequency 60 11 10 13 7 6 5 8

Find the median of the distribution using the ascending cumulative frequency curve.

• A12.8
• B21
• C34
• D6.5

### Example

The following table shows the frequency distribution for the scores of 60 students in an exam:

 Sets Total Frequency 60 11 10 13 7 6 5 8

Find the median of the distribution using the ascending cumulative frequency curve.

• A12.8
• B21
• C34
• D6.5

### Solution

First, form an ascending cumulative frequency table.

Upper boundaries of setsFrequency
less than 20
less than 611
less than 1021
less than 1434
less than 1841
less than 2247
less than 2652
less than 3060

Then use the table to draw an ascending cumulative frequency curve.

To identify the median, draw a horizontal line on the cumulative frequency curve that passes through the order of the median, or half of the frequency total. For this data, the frequency total is 60, so we will draw the horizontal line to pass through the order of the median 30. The related score along the -axis is the median.

The score that corresponds to a frequency of 30 is 12.8. So, the median of distribution is 12.8.

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