Grouped Data Standard Deviation Calculator

How it is calculated

Enter the class midpoints (m) and the frequency (f) of each class, separated by spaces or commas, with the same number of entries in both lists. With N = Σf, the tool computes the weighted mean x̄ = Σ(f·m) ÷ N and the population variance σ² = Σ f·(m − x̄)² ÷ N. The standard deviation is σ = √σ². It divides by N, not N − 1, so it treats the table as the whole population. Every value in a class is assumed to sit at its midpoint, so the result is an estimate. Frequencies are counts of observations, so they must be whole numbers and not negative; a fractional or negative frequency, lists of different lengths, or a total frequency of zero show no result. Midpoints may be negative or decimal.

Common mistakes

• Entering the class limits (0–10) or the class width instead of the midpoints. The midpoint of 0–10 is 5, and there must be one midpoint per class.
• Giving lists of different lengths, such as 5 midpoints and 4 frequencies. Each midpoint needs exactly one frequency, or there is no result.
• Entering relative frequencies such as 0.1, 0.2, 0.4 or percentages with decimals. Frequencies must be whole counts, so fractional values show no result; use the original counts from the table.
• Expecting the sample standard deviation. This tool divides by N, the population version; for a sample the usual formula divides by N − 1, which gives a slightly larger value.
• Typing a decimal comma. Commas separate numbers in these lists, so 12,5 is read as 12 and 5; write 12.5.