Mean from a Frequency Table

When data comes as a frequency table, each value is listed once together with how often it occurs. The mean is still the total divided by the count — but you must not add the values once each. A value that occurs ten times contributes ten times over, so weight each value by its frequency:

\text{mean} = \frac{\sum (\text{value} \times \text{frequency})}{\sum \text{frequency}}

Add a column for f \times x (frequency times value), total it, and divide by the total frequency. For example, the value 1 occurs 4 times, 2 occurs 6 times and 3 occurs 10 times:

Value (x)	Frequency (f)	f \times x
1	4	4
2	6	12
3	10	30
Total	20	46

The total frequency is \sum f = 4 + 6 + 10 = 20 (there are 20 items in all), and \sum (f \times x) = (1\times 4) + (2\times 6) + (3\times 10) = 46. So the mean is 46 \div 20 = 2.3.

Add an f \times x column — each value multiplied by its frequency.
The mean is \text{mean} = \frac{\sum (f \times x)}{\sum f}.
\sum f is the total number of items, so the frequencies must sum to the size of the data set.
This is a weighted average: a value that occurs more often pulls the mean toward itself.