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Statistics calculator

Enter a data set to get mean, median, minimum and maximum, with the sorting process and a bar chart

Formula

\bar x=\frac{\sum x_i}{n},\quad \tilde x=x_{(\frac{n+1}{2})}

\bar=\frac\sum x_i

DataCount n

Separate values with commas, spaces or newlines; decimals and negatives are supported.

Presets

Mean81.9

Median83

Minimum66

Maximum95

n10Σx819R29

Data distribution Mean Median

Each bar is one value, the dashed line is the mean

Sorted ascending

Steps

6 / 6

1Given
$n=10$
Collect the given quantities first.
2Add contributions
$\sum x_i=66+70+74+78+81+\cdots+92+95=819$
3mean
$\bar x=\frac{\sum x_i}{n}=\frac{819}{10}=81.9$
4Midline
$\tilde x=\frac{x_{5}+x_{6}}{2}=\frac{81+85}{2}=83$
The midline is half the sum of the bases.
5minmax
$\min=66,\quad \max=95,\quad R=95-66=29$
6Result
$\bar x=81.9,\ \tilde x=83,\ \min=66,\ \max=95$
Collect all computed quantities.

Concept

The mean describes the overall level, the median the middle position; both can be shifted by extreme values, but the median is more robust.

After sorting, the median is the middle value for an odd count, or the mean of the two middle values for an even count.

Going further

Mean or median: For skewed data such as incomes or house prices the median is fairer; for scores and measurements the mean is usual.
Mode: The most frequent value is the mode; a data set can have several modes or none.
Range and variance: Max minus min is the range, measuring spread; variance measures how far values sit from the mean.

Common mistakes

Sort before taking the median - a common mistake.
With an even count the median may not be one of the original values.
The mean is pulled by outliers; check the distribution before trusting it.

Page keywordsstatistics calculatormeanmedianminimum maximumhow to calculate the meanhow to find the medianmedian with even countaverage score calculatorrange of a data set

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