Statistics Calculator
Paste a list of numbers to get the averages, spread, quartiles and a box plot, with the working shown.
Separate them with commas, spaces or new lines.
About this tool
Paste a list of numbers and this statistics calculator works out the count, sum, mean, median, mode, range, minimum, maximum, lower and upper quartiles and the interquartile range, plus the population and sample standard deviation and variance. It draws a box plot with any outliers marked (values more than 1.5 × IQR beyond the quartiles) and a dot plot of every value, and it shows the working for the mean, the median and the standard deviation step by step.
Tips
- The median is in position (n + 1) / 2 once the values are in order. With an even count, it is halfway between the two middle values.
- An outlier pulls the mean towards it but hardly moves the median, so the median is the better average for skewed data.
- Different textbooks find quartiles in slightly different ways. If your answer is out by a little, switch the quartile method.
FAQ
- What is the difference between population and sample standard deviation?
- Both measure how spread out the data is. The population SD divides by n. The sample SD divides by n − 1, which makes it slightly larger and gives a better estimate of the spread of the whole population from a sample.
- How are the quartiles worked out?
- The values are put in order and split into a lower and an upper half. Q1 is the median of the lower half and Q3 the median of the upper half. With an odd count you can include the median in both halves or leave it out of both; the calculator lets you choose.
- How does it decide what an outlier is?
- Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR counts as an outlier. It is shown as a separate dot on the box plot, and the whiskers stop at the furthest values that are not outliers.