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Simple Calculators

Statistics Calculator

Enter a list of numbers to instantly compute mean, median, mode, standard deviation, and more

Statistics Calculator

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Quick summary

A statistics calculator computes descriptive statistics for a set of numbers. Descriptive statistics summarize the central tendency (mean, median, mode), spread (variance, std deviation, range), and distribution (quartiles) of a dataset.

Reviewed by Simple Calculators TeamLast reviewed

How to use this calculator

  1. Enter the inputs requested by the calculator.
  2. Choose the units or options that match your situation and review the assumptions.
  3. Run or update the calculation to see the result.
  4. Review the result, breakdown, and formulas shown on the page.
  5. Check the inputs, units, dates, and limitations before saving or sharing the result.

Statistics Formulas & Examples

Mean (Average)

xˉ=∑xin\bar{x} = \frac{\sum x_i}{n}
Σxᵢ
Sum of all values
n
Count of values

Worked example

Dataset: 2, 4, 6, 8, 10

Given
Σxᵢ = 30
n = 5
Calculation
xˉ=30/5\bar{x} = 30 / 5
Result
= 6

Standard Deviation

σ=∑(xi−xˉ)2n\sigma = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n}}
xᵢ
Each value in the dataset
x̄
Mean of the dataset
n
Count of values

Worked example

Dataset: 2, 4, 6, 8, 10 (mean = 6)

Given
x̄ = 6
n = 5
Calculation
σ=(16+4+0+4+16)/5\sigma = \sqrt{(16+4+0+4+16)/5}
Result
≈ 2.828

Interquartile Range (IQR)

IQR=Q3−Q1IQR = Q_3 - Q_1
Q1
25th percentile (lower quartile)
Q3
75th percentile (upper quartile)

Worked example

Dataset: 1, 3, 5, 7, 9, 11, 13

Given
Q1 = 3
Q3 = 11
Calculation
IQR=11−3IQR = 11 - 3
Result
= 8

Frequently asked questions

What is the difference between mean and median?

The mean is the arithmetic average: sum all values and divide by count. The median is the middle value when sorted. For skewed data or datasets with outliers, the median is often more representative. For example, in [1, 2, 3, 4, 100], the mean is 22 but the median is 3.

What does standard deviation measure?

Standard deviation measures how spread out values are from the mean. A low std dev means values cluster closely around the mean; a high std dev means they are spread out. This calculator uses population standard deviation (divide by n, not n-1).

How are quartiles calculated?

Quartiles divide sorted data into four equal parts. Q1 (25th percentile) is the median of the lower half; Q3 (75th percentile) is the median of the upper half. The IQR (Q3-Q1) captures the middle 50% of data.

What is the mode?

The mode is the most frequently occurring value. A dataset can have no mode (all values unique), one mode (unimodal), or multiple modes (bimodal/multimodal). If every value appears once, no mode is reported.

Key terms

Mean
The arithmetic average of a set of numbers: sum / count.
Median
The middle value in a sorted dataset.
Variance
The average of squared deviations from the mean.
IQR
Interquartile Range: Q3 minus Q1, measuring the spread of the middle 50% of data.

Methodology, sources & limitations

This page shows the formula, assumptions, and limitations used for this estimate. Rates, thresholds, and other time-sensitive inputs can change, so verify them against the relevant official source before relying on a result.

For our review approach and the primary sources we consult, see the methodology and source policy. If you spot an outdated figure or formula, please contact us with a correction.