Quick answer: For a discrete frequency table, mean = Σfx/Σf. Multiply each value x by its frequency f, add those products, and divide by the number of observations, not by the number of rows.
Worked example
Values 2, 4, 6 have frequencies 3, 2, 5. Find the mean.
- Products fx are 6, 8 and 30.
- Σfx = 44 and Σf = 10.
- Mean = 44/10 = 4.4.
Check the result
The mean is between the smallest value 2 and largest value 6. Expanding the data would give ten observations with total 44.
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Common mistake to avoid
Averaging 2, 4 and 6 directly ignores unequal frequencies. For grouped intervals, class midpoints give an estimated mean instead.
Try it yourself
1. Values 1 and 5 have frequencies 2 and 3. Find mean. 2. If every observation increases by 2, how does the mean change?
Answers and reasoning
1. (1×2 + 5×3)/5 = 17/5 = 3.4. 2. The mean increases by 2, since the total increases by 2 times the observation count.
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