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Frequency Table

Data that comes as a table: each value with how often it occurs, or classes such as 40–50 with a count. Get the mean, median, mode, standard deviation and quartiles without typing out every single value.

StatisticsGrouped dataHistogram
Inputs
Input examples
One row per line. Values with counts: the value, then how often it occurs, e.g. 3, 6. Class intervals: the class, then its count, e.g. 40-50, 3; a value on a boundary belongs to the higher class. For classes the calculator uses the class midpoints, so the results are estimates.

What is a Frequency Table?

A frequency table lists each value once, with its frequency f: how many times it occurs. The mean is then a weighted average, Σf·x / Σf, and the same goes for the standard deviation.

With grouped data you only know how many values fall in each class, not the values themselves. The usual approach is to treat every value as if it sat at the class midpoint. The median and quartiles are estimated by assuming the values are spread evenly through their class.

n= Σf
midpoint(lower + upper) / 2
modal classthe highest count
groupedresults are estimates

Bar Chart

n
count
mean
median
Result
Enter the values above

Your Frequency Table

with cumulative counts
ValueCount fCumulative%Cumulative %

Worked Techniques

Mean from a Table

Multiply each value by its count, add up, and divide by the total number of values.

Example: children per family 0×5, 1×9, 2×12, 3×6, 4×3: 63 / 35 = 1.8.
Mean from Classes

Use the midpoint of each class as its value. The result is an estimate: the true values inside a class are not known.

Example: scores in classes of 10: mean ≈ 2770 / 40 = 69.25.
Median from Classes

Find the class that holds the middle value. L is its lower boundary, F the count below it, f its own count and w its width.

Example: 

Sources & Verification

References
  1. D. C. Montgomery & G. C. Runger, Applied Statistics and Probability for Engineers, 6th ed., Wiley, 2013 — Ch. 6 (Descriptive Statistics).