Averages from tables

Objective. Calculate means from frequency tables.

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2. Worked example
3. Practice
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Learn: the key idea

To calculate the mean from a frequency table, multiply each data value by its frequency, add all these products together, then divide by the total frequency. This weights each value according to how often it occurs rather than treating every row equally. Example: for values 2, 3 and 5 with frequencies 4, 1 and 2, compute (2×4) + (3×1) + (5×2) = 8 + 3 + 10 = 21, then divide by the total frequency 4+1+2=7, giving a mean of 3. Always check the total frequency carefully, since dividing by the wrong number is a common source of error.

Worked example

A frequency table shows the number of pets owned: 0 pets (frequency 3), 1 pet (frequency 5), 2 pets (frequency 2). Find the mean number of pets.

1 $Multiply each value by its frequency: 0\times3=0, 1\times5=5, 2\times2=4.$
2 $Add these products together: 0 + 5 + 4 = 9.$
3 $Add the frequencies to find the total number of pupils: 3 + 5 + 2 = 10.$
4 $Divide the total by the frequency sum: 9 \div 10 = 0.9.$

Answer: 0.9 pets

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Common mistake. Pupils sometimes divide by the number of rows in the table instead of the total frequency; always sum all the frequency values first to get the correct divisor for the mean.

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