Descriptive statistics for a list of numbers
Descriptive statistics summarise a set of numbers in a few figures: where the middle is, how spread out the values are, and what the extremes look like. They are the first step in looking at test scores, survey answers, response times, sales figures or lab measurements.
Paste a list of numbers and this tool calculates the count, sum, mean, median, mode, minimum, maximum, range, quartiles, and both the population and the sample variance and standard deviation.
How to use it
- Paste or type numbers separated by commas, spaces or line breaks.
- Read the summary table, which updates as you type.
- Choose the right variance: population if your list is the whole group, sample if it is a sample from a larger group.
- Copy the figures you need into your report.
Example: eight values
2, 4, 4, 4, 5, 5, 7, 9
Mean: 5 Median: 4.5 Mode: 4 Stdev (population): 2 Stdev (sample): 2.1381
The median sits between the 4th and 5th values, 4 and 5. The sample standard deviation is larger because it divides by 7 instead of 8.
Mean, median and mode
The mean is the sum divided by the count. The median is the middle value once the list is sorted, or the average of the two middle values. The mode is the value that appears most often, and there can be several. When a few very large values pull the mean up, as with incomes or house prices, the median describes a typical value better.
Population or sample?
Variance measures the average squared distance from the mean, and the standard deviation is its square root, in the same units as the data. If your numbers are the entire group you care about, every employee or every product in a batch, use the population figures, which divide by n. If they are a sample used to estimate a larger group, use the sample figures, which divide by n − 1. That correction, named after Friedrich Bessel, makes the estimate unbiased. In Excel these are STDEV.P and STDEV.S.
Quartiles
Q1 and Q3 split the sorted data into quarters: a quarter of the values lie below Q1 and a quarter above Q3. The middle half lies between them, and Q3 − Q1 is the interquartile range, a spread measure that ignores outliers. This tool interpolates between neighbouring values, the method of Excel's QUARTILE.INC; other software may use a slightly different method, so small differences are normal.
Questions
Can I paste a column from a spreadsheet?
Yes. Values separated by line breaks work, and anything that is not a number is skipped.
Why is there no sample variance for a single value?
Dividing by n − 1 needs at least two values. With one value, the spread of the wider group cannot be estimated.
Is my data uploaded?
No. All calculations happen in your browser.