Turn raw data into a frequency table, or enter class intervals with frequencies to find the mean, median, mode and standard deviation of grouped data.
Separate numbers with commas, spaces or line breaks. You can paste a column from Excel or Sheets. 20 values read.
Total frequency N = 20. Modal class 30–40. Population SD 9.
From the raw values exactly: mean 38, median 37.5, SD 8.8852. Grouped values are estimates.
| Class | Midpoint m | f | Relative f | Cumulative f | f·m | f(m − x̄)² |
|---|---|---|---|---|---|---|
| 20 – 30 | 25 | 4 | 20% | 4 | 100 | 676 |
| 30 – 40 | 35 | 8 | 40% | 12 | 280 | 72 |
| 40 – 50 | 45 | 6 | 30% | 18 | 270 | 294 |
| 50 – 60 | 55 | 2 | 10% | 20 | 110 | 578 |
| Σ | 20 | 100% | 760 | 1,620 | ||
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x̄ ≈ Σf·m ÷ Σf · Median ≈ L + ((N/2 − CF) ÷ f)·h · Mode ≈ L + (f₁ − f₀)/(2f₁ − f₀ − f₂)·h
Grouped formulas trade a little accuracy for a compact summary. If you still have the raw values, the exact mean, median and mode and standard deviation are always better; the raw-data mode here shows both side by side so you can see the size of the approximation. To chart the table, use the histogram maker.
Find the range of the data, choose a number of classes (often 5 to 15), and pick a convenient class width that covers the range. List the class intervals, then count how many values fall in each. Add columns for midpoints, relative frequency (count ÷ total) and cumulative frequency as needed.
Multiply each class midpoint by its frequency, add these products, and divide by the total frequency: x̄ ≈ Σ(f·m) ÷ Σf. It is an estimate, because every value in a class is treated as if it sat at the midpoint.
Locate the median class, the first class whose cumulative frequency reaches N/2. Then interpolate: median = L + ((N/2 − CF) ÷ f) × h, where L is the lower boundary of that class, CF the cumulative frequency before it, f its frequency and h the class width.
The modal class is the one with the highest frequency. An estimate of the mode inside it is L + (f₁ − f₀) ÷ (2f₁ − f₀ − f₂) × h, where f₀ and f₂ are the frequencies of the classes before and after.
Relative frequency is a class’s share of the total (frequency ÷ N), often shown as a percent. Cumulative frequency is the running total up to and including that class; the last one always equals N.
Use the midpoints: s² ≈ Σf(m − x̄)² ÷ (N − 1) for a sample, or divide by N for a population, then take the square root. The table on this page shows both.