High School

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------------------------------------------------ Find the mean of the following distribution:

Class:
10-25, 25-40, 40-55, 55-70, 70-85, 85-100

Frequency:
2, 3, 7, 6, 6, 6

Answer :

Final answer:

The mean of this frequency distribution is 62.

Explanation:

Finding the Mean of a Frequency Distribution

To find the mean of the given frequency distribution, we multiply each class by its frequency and then sum these products. After that, we divide this sum by the total number of data points (sum of frequencies). In this case, we need the midpoints of each class interval to represent that class.

The midpoints for the classes are:

10-25: 17.525-40: 32.540-55: 47.555-70: 62.570-85: 77.585-100: 92.5

We then calculate the product of each midpoint and its frequency:

17.5 × 2 = 3532.5 × 3 = 97.547.5 × 7 = 332.562.5 × 6 = 37577.5 × 6 = 46592.5 × 6 = 555

The sum of these products is 35 + 97.5 + 332.5 + 375 + 465 + 555 = 1860.

The total frequency is 2 + 3 + 7 + 6 + 6 + 6 = 30. Therefore, the mean of the distribution is:

× = 1860 ÷ 30 = 62

The mean of this frequency distribution is 62.

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