Grouped Data Mean Calculator

How it is calculated

When data are only available as classes, each class is represented by its midpoint m, the value halfway between its lower and upper boundary. The estimated mean is mean = Σ(f × m) ÷ Σf, where f is the frequency of the class. The tool multiplies each midpoint by its frequency, adds the products and divides by the total frequency. Midpoints and frequencies are two lists, separated by commas or spaces, with the same number of entries in the same order. Frequencies are counts of observations, so each must be a whole number of zero or more; a fractional or negative frequency, mismatched lists or a total frequency of zero shows no result. Midpoints may be any numbers. Use a dot for decimals, since a comma separates entries. The answer is an estimate and will differ a little from the mean of the raw data.

Common mistakes

• Entering the class boundaries instead of the midpoints. For a class 10–20 enter 15, not 10 or 20, otherwise the mean is biased up or down.
• Giving the lists different lengths, for example four midpoints and five frequencies. The counts must match or there is no result.
• Entering a percentage or relative frequency such as 10.5 or 0.25 as a frequency. Frequencies are whole counts, so a fractional value shows no result; enter the actual number of observations.
• Typing the classes in a different order in the two lists, so that a midpoint is paired with the wrong frequency.
• Entering cumulative frequencies instead of the class frequencies. The formula needs the count in each class alone, not the running totals.