Advanced options
What The Average Calculator Works Out
- Mean: the total divided by the count, the everyday "average" and the right tool for evenly spread data. In the sample 1, 2, 2, 3, 4 the mean is 2.4.
- Median: the middle value once the numbers are sorted, or the midpoint of the middle two. A few extreme values drag the mean around but leave the median alone, which is why UK house prices and salaries are reported as medians: high earners pull the mean well above what a typical worker gets.
- Mode: the most frequent value, useful for categories and common sizes. A dataset can have several modes or none.
- Range, sum and count: largest minus smallest is the crudest measure of spread; the sum and count are the raw ingredients of the mean, and together they sanity-check any average you are quoted. Numbers can be pasted straight from a spreadsheet column.
- Standard deviation (advanced): the square root of the average squared distance from the mean, the standard measure of spread. Population form divides by n when you have every value; sample form divides by n - 1 when the numbers are a sample of something bigger, which is what GCSE and A-level statistics and Excel's STDEV.S use. The variance (deviation squared) is shown underneath.
- Weighted mean (advanced): each value multiplied by its weight, summed and divided by the total weight. It is how module marks with different credit values are combined into a degree average and how a price index is built.
- Trimmed mean (advanced): removes a chosen percentage of values from each end before averaging, so a single rogue reading or a typo cannot distort the result. Judges' scores in diving and gymnastics work this way.
- Geometric mean (advanced): the nth root of the product of the values, the correct average for growth rates, interest rates and ratios: 10% growth then 30% growth averages 19.6% a year, not 20%. It needs all values to be positive.
- Interquartile range (advanced): the gap between the first and third quartiles (the medians of the lower and upper halves), covering the middle 50% of the data. It ignores outliers entirely and is the box in a box plot.
- Decimal places (advanced): choose 2, 4 or 6 places for every result.