Statistics Calculator
Paste a list of numbers. The tool sorts them for the median, counts frequencies for the mode, and shows every squared deviation from the mean for the variance. Choose population (divide by n) or sample (divide by n − 1) — the divisor used is shown clearly. Results are exact fractions where possible.
Step-by-step
waitingFill in the fields and press Solve. The full method will appear here, one numbered step at a time.
Worked example
Find the mean, median, mode, variance and standard deviation of 4, 8, 6, 5, 3, 8 as a population.
- 1.
Count the values.
n = 6
- 2.
Add them up.
Σx = 4 + 8 + 6 + 5 + 3 + 8 = 34
- 3.
Mean = sum ÷ count.
x̄ = 34 ÷ 6 = 17/3 (≈ 5.666667)
- 4.
Sort the values from smallest to largest for the median and range.
3, 4, 5, 6, 8, 8
- 5.
n is even, so the median is the average of the two middle values (positions 3 and 4).
median = (5 + 6) ÷ 2 = 11/2
- 6.
Count how often each value appears. The highest frequency is 2.
mode = 8
- 7.
Range = largest − smallest.
8 − 3 = 5
- 8.
For the variance, subtract the mean from each value and square the result.
(4 − (17/3))² = 25/9 (8 − (17/3))² = 49/9 (6 − (17/3))² = 1/9 (5 − (17/3))² = 4/9 (3 − (17/3))² = 64/9 (8 − (17/3))² = 49/9
- 9.
Add the squared deviations.
Σ(x − x̄)² = 64/3
- 10.
Population variance: divide by n = 6.
σ² = 64/3 ÷ 6 = 32/9 (≈ 3.555556)
- 11.
Standard deviation is the square root of the variance.
σ = √(32/9) ≈ 1.885618
Answer: n = 6 sum = 34 mean = 17/3 median = 11/2 mode = 8 range = 5 population variance σ² = 32/9 standard deviation ≈ 1.885618
Note: Choose population (÷ n) or sample (÷ n − 1); the steps say which is used.
Use “Load worked example” above to run this in the solver.
Related formulas
The formulas this tool uses, each explained with symbols, conditions and its own example in the Formula Library.