How it works

For a frequency table, the mean is found by multiplying each value by its frequency, summing these products, and dividing by the total frequency. The median is the middle value once data is placed in order (using cumulative frequency for grouped data), the mode is the most frequent value, and the range is the difference between the highest and lowest values.

The method

1. 1.Multiply each value (or midpoint) by its frequency
2. 2.Sum these products and sum the frequencies
3. 3.Divide the sum of products by the total frequency for the mean
4. 4.Use cumulative frequency to locate the median position

Worked example

Find the mean number of pets: 0 pets (freq 3), 1 pet (freq 5), 2 pets (freq 2).

1. Sum = 0x3 + 1x5 + 2x2 = 9
2. Total frequency = 10, mean = 9/10 = 0.9

Worked example

Find the median from the same data.

1. Total frequency = 10, median position is between 5th and 6th value
2. Both are 1, so median = 1

Common mistakes

• Dividing by the number of rows instead of the total frequency when finding the mean
• Using the frequency instead of the value when identifying the mode
• Using the midpoint of the class incorrectly, or forgetting to use midpoints for grouped data