How to use the Mean Median Mode of Grouped Data Calculator
- 1. Enter your classesType one class per line with its frequency, like 10-20, 8.
- 2. CalculatePress the button to get the mean, median and mode together.
- 3. Check the workingUse the table of midpoints, f·x and cumulative frequency in your answer.
Formulas for grouped data
- Mean = Σ(f × x) ÷ Σf, where x is the class midpoint.
- Median = L + ((N/2 − CF) ÷ f) × h, where L is the lower boundary of the median class, CF the cumulative frequency before it, f its frequency and h its width.
- Mode = L + ((f₁ − f₀) ÷ (2f₁ − f₀ − f₂)) × h, using the modal class and the classes on either side.
Worked example (the default data): classes 0-10, 10-20, 20-30, 30-40, 40-50 with frequencies 5, 8, 15, 10, 2. N = 40 and Σfx = 960, so the mean is 24. N/2 = 20 falls in 20-30 (cumulative 13 before it), so the median is 20 + (7 ÷ 15) × 10 = 24.6667. The modal class is also 20-30: 20 + (7 ÷ 12) × 10 = 25.8333.
Exclusive vs inclusive classes
Board exam questions often give classes like 10-19, 20-29. These have a gap of 1 between them, so the true class boundaries are 9.5-19.5, 19.5-29.5 and so on. The calculator spots an even gap and adjusts the boundaries for the median and mode, and it tells you it did so. The mean does not change, because midpoints stay the same.
Use the empirical relation Mode ≈ 3 Median − 2 Mean as a quick sense check; for the example it gives 26, close to the 25.83 from the formula. If two classes share the highest frequency, the data is bimodal and the formula is less meaningful. Raw data instead of a table? Use the frequency distribution table maker first, or the average calculator for ungrouped numbers.
Frequently asked questions
Is the grouped mean the same as the real mean?
Not exactly. It assumes every value sits at its class midpoint, so it is an estimate of the mean of the raw data.
What if the modal class is the first class?
The frequency before it is taken as 0, which is the standard textbook rule.
Is the Mean Median Mode of Grouped Data Calculator free?
Yes, the Mean Median Mode of Grouped Data Calculator is free. The first time you see your first result, you are asked for your name and WhatsApp number once. After that, this and every other Uncodemy tool opens straight away without the form.