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📊 Mean, median and mode step by step
Type your data or the frequency table from the exercise. You will see the full table, every measure with its steps and the bar chart.
Data
Separate them with commas and a space (3, 5, 7), semicolons or spaces. Decimals with a point: 2.5 3.1.
Examples:
Data read, sorted: 3 · 5 · 7 · 7 · 9
Standard deviation
2√26/5 ≈ 2.04
Frequency table
| xᵢ | fᵢ | Fᵢ | hᵢ | % |
|---|
| 3 | 1 | 1 | 0.2 | 20 % |
| 5 | 1 | 2 | 0.2 | 20 % |
| 7 | 2 | 4 | 0.4 | 40 % |
| 9 | 1 | 5 | 0.2 | 20 % |
| N | 5 | |
Mean (x̄)
- Add up all the data: each value times how often it appears.
- 3 + 5 + 7·2 + 9 = 31
- Divide by the number of data values, N = 5: x̄ = 31 / 5 = 6.2
Median (Me)
- With the data sorted, the median is the middle value. There are N = 5 values, which is odd.
- Middle position: (N + 1) / 2 = 3. Value number 3 is 7.
- To find a position, look for the first row whose cumulative frequency (Fᵢ) reaches that number.
- Me = 7
Mode (Mo)
- The most repeated value is 7, 2 times: Mo = 7.
Range
- Maximum − minimum = 9 − 3 = 6
Variance and standard deviation
- How far the data are from the mean, on average. For each value: its distance to the mean, squared, times its frequency.
- σ² = Σ fᵢ·(xᵢ − x̄)² / N = ((3 − 6.2)² + (5 − 6.2)² + 2·(7 − 6.2)² + (9 − 6.2)²) / 5 = 4.16
- σ = √σ² = 2√26/5 ≈ 2.04