Enter your class intervals and frequencies into the Grouped Data Mean Calculator to compute the mean of a frequency distribution table. Add up to 10 class-frequency pairs, and the calculator returns the mean, total frequency, and a breakdown of midpoints and weighted values — using the standard midpoint method.
Mean (x̄)
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Total Frequency (Σf)
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Sum of f·x (Σfx)
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Number of Classes
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The mean of grouped data is calculated as x̄ = Σ(f · x) / Σf, where x is the midpoint of each class interval and f is the corresponding frequency. The midpoint of a class is found by averaging its lower and upper bounds: x = (lower + upper) / 2.
When data is grouped into class intervals, the exact individual values are unknown. The midpoint of each class is used as the best estimate for all values within that interval. This midpoint method gives a reasonable approximation of the true mean.
Grouped data refers to data that has been organized into class intervals (ranges) along with the count (frequency) of observations falling within each class. For example, knowing that 12 students scored between 20 and 30 on a test is grouped data — we know the range but not each individual score.
For raw (ungrouped) data, you simply sum all values and divide by the count. For grouped data, you don't have individual values — only class ranges and frequencies. So you approximate each value using the class midpoint, then apply the weighted mean formula Σ(f · x) / Σf.
This calculator supports up to 6 class intervals. Fill in only the classes that apply to your data — any class left blank will be ignored in the calculation. Make sure every filled class has both bounds and a frequency entered.
The order doesn't affect the final mean result since the formula sums all f·x products regardless of order. However, entering classes in ascending order makes the breakdown table easier to read and verify.
This calculator uses each class's lower and upper bounds to compute the midpoint independently, so gaps between classes won't cause errors — each class is treated separately. Overlapping intervals, however, may produce misleading results since some values would be counted in multiple classes.
Open-ended intervals don't have a defined upper or lower bound, so you'll need to estimate a reasonable boundary to use this calculator. For example, if the last class is '50 and above', you might use 50–60 based on context. The result will be an approximation.