Grouped Data Calculator
Find the mean, median, mode and standard deviation of grouped data, with the direct, assumed-mean or step-deviation method, a working table and ogives.
About the Grouped Data Calculator
Grouped data gives frequencies for class intervals instead of single values. Each class is represented by its class mark, the mid-point. The three mean methods always give the same answer: the assumed-mean and step-deviation methods just keep the arithmetic small.
The median uses the class where the cumulative frequency first reaches N/2, and the mode uses the class with the highest frequency.
The formula
x̄ = a + h × Σfu ÷ Σf, Median = l + ((N/2 − cf)/f) × h, Mode = l + ((f₁ − f₀)/(2f₁ − f₀ − f₂)) × h
- a
- assumed mean
- h
- class width
- u
- (x − a)/h
- l
- lower boundary of the median or modal class
- cf
- cumulative frequency before the median class
- f₁, f₀, f₂
- frequencies of the modal class and the classes before and after
Worked example
Classes 0-10 … 40-50, frequencies 5, 8, 15, 10, 7
- a = 25, h = 10: Σfu = 5(−2) + 8(−1) + 0 + 10(1) + 7(2) = 6
- x̄ = 25 + 10 × 6 ÷ 45 = 26.33…
Questions people ask
Why do the three methods give the same mean?
They're the same formula rearranged: the assumed-mean and step-deviation methods subtract a and divide by h, then undo it at the end.
What about inclusive classes like 1-10, 11-20?
The calculator moves each boundary half the gap (0.5 here), giving 0.5-10.5, 10.5-20.5, before using the median and mode formulas, as textbooks do.
Where's the ogive?
The less-than and more-than ogives are drawn below. They cross at the median.