# 5.9.4. Representing Data by the Histogram and the Frequency Polygon

Use the frequency polygon below, which represents the marks of a group of students in a test, to complete the frequency table.

 Sets Total Frequency 60 0– 10– 20– 30– 40– 50– 60–
• A4, 7, 10, 11, 13, 8, 7
• B4, 7, 10, 11, 13, 7, 8
• C5, 7, 10, 11, 13, 8, 7
• D4, 10, 7, 11, 13, 8, 7

### Example

Use the frequency polygon below, which represents the marks of a group of students in a test, to complete the frequency table.

 Sets Total Frequency 50 0– 10– 20– 30– 40– 50– 60–

### Solution

A frequency polygon graphs information from a frequency table by plotting the mid-point of each set and joining the points by a line.

The mid-point for 0 is 5, the mid-point for 10 is 15, the mid-point for 20 is 25, the mid-point for 30 is 35, the mid-point for 40 is 45, the mid-point for 50 is 55, and the mid-point for 6070 is 65. Look along the vertical axis to find the related frequencies: 2, 4, 9, 12, 14, 6, and 3.

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