Frequency weighting
SAT glossary · Course Foundations
Definition
Computing a mean from a display by weighting each value by its count: (1(3)+2(5)+3(8)+4(4))/(20) = 2.65. Ignoring the frequencies gives 2.5, the mean of 1,2,3,4 — and the check is that a mean outside the range of the data is always an arithmetic error.
Frequency weighting in plain English
When data is shown as a table of values along with how many times each one shows up (its frequency), you can't just average the plain list of values — you have to give each value 'extra weight' equal to how often it appears. For example, if the data is 1,2,3,4 appearing 3, 5, 8, and 4 times respectively, you calculate the mean as (1(3)+2(5)+3(8)+4(4))/(20)=2.65 — using the total COUNT of all data points (20) as your denominator, not just the number of distinct values (4). If you ignore the frequencies and just average 1,2,3,4 plainly, you'd wrongly get 2.5. A useful sanity check: the true mean should always land somewhere WITHIN the range of the actual data values.
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