Describe your data in a few numbers
Whether you are analysing exam marks, monthly sales, survey answers, cricket scores or lab measurements, a handful of statistics tells you most of what you need to know: where the centre of the data is, how spread out it is, and whether there are unusual values. This calculator works them all out at once from a simple list of numbers.
How to use the calculator
- Paste or type your numbers, separated by commas, spaces or new lines. You can paste a column straight from Excel.
- All results update instantly, and your data is shown sorted below.
Measures of the centre
- Mean (average): the sum divided by the count. For the sample marks: 811 ÷ 10 = 81.1.
- Median: the middle value when sorted (or the average of the two middle values). It is not affected by a few extreme values, so it is better for things like incomes and house prices.
- Mode: the value that appears most often. In the sample, 85 appears three times.
Measures of spread
sample variance s² = Σ(x − mean)² ÷ (n − 1)
population variance σ² = Σ(x − mean)² ÷ n
standard deviation = √variance
Standard deviation is the typical distance of values from the mean. A small value means the data is clustered together; a large value means it is spread out. Use the sample version when your numbers are a sample from a bigger group (most real situations), and the population version when you have every value in the group.
Quartiles split the sorted data into four equal parts. Q1 is the 25th percentile and Q3 the 75th. The interquartile range (IQR = Q3 − Q1) covers the middle half of the data. Values more than 1.5 × IQR below Q1 or above Q3 are often treated as outliers.
Frequently asked questions
Why are there two standard deviations?
Dividing by n − 1 (Bessel's correction) gives a fairer estimate when you only have a sample. For large datasets the two values are almost the same.
Which quartile method is used?
The linear interpolation method, the same as Excel's QUARTILE.INC and most calculators. Some textbooks use slightly different methods, which can give different values for small datasets.
Can I enter decimals and negative numbers?
Yes, both are supported.