A list of numbers says little until you summarize it. Paste your data and this calculator gives the center (mean, median, mode), the spread (range, interquartile range, standard deviation, variance) and the five-number summary you need for a box plot.
How to Use It
- Paste or type your Numbers, separated by commas, spaces or new lines.
- Press Calculate.
- Read the mean at the top, the other statistics below it, and the five-number summary table at the end.
How It Works
The mean is the sum divided by the count, and the median is the middle value of the sorted list (the average of the two middle values when the count is even). Q1 and Q3 are the medians of the lower and upper halves; with an odd count, the median is left out of both halves.
The standard deviation measures how far values typically sit from the mean. For a whole population of values:
For a sample of values standing in for a bigger group, divide by instead:
The variance is the standard deviation squared.
Worked Example
For 2, 4, 4, 4, 5, 5, 7, 9: the sum is 40 and the count 8, so the mean is 5. The middle two values are 4 and 5, so the median is 4.5, and 4 appears most, so it’s the mode.
The squared distances from 5 add up to , so:
The halves are 2, 4, 4, 4 and 5, 5, 7, 9, so Q1 = 4, Q3 = 6 and the IQR is 2.
Tips and Common Mistakes
- Sample or population? Most class data sets and experiments are samples; use s unless you truly have every member of the group.
- Outliers pull the mean. When one value is far from the rest, the median and IQR describe the data better.
- Sort before finding the median by hand. The middle of an unsorted list isn’t the median.
- Quartile methods vary. Other software can give slightly different Q1 and Q3; check which method your class uses.
- Check the count. If it’s not the number of values you meant to enter, look for a missing separator.