About the statistics calculator
This statistics calculator summarises a list of numbers: count, sum, mean, median, mode, minimum, maximum, range, quartiles, interquartile range, standard deviation, variance, standard error, geometric and harmonic means, and a frequency table.
Paste or type your data once and see the whole picture in one place.
Who should use the statistics calculator
- Students working on statistics assignments.
- Analysts doing a quick first look at a data set.
- Anyone who needs a single table of descriptive statistics.
How to use the statistics calculator: what each input means
- Data values
- Numbers separated by commas, spaces or new lines, up to 10,000 values.
How the statistics calculator works: method and formula
The data are sorted, then each statistic is calculated from the full list. The median is the middle value (or the average of the two middle values). Quartiles use the median-of-halves method: the lower quartile is the median of the lower half and the upper quartile is the median of the upper half, with the median itself left out of both halves when the count is odd.
- Mean
- x̄ = Σx ÷ n
- Interquartile range
- IQR = Q3 − Q1
- Geometric mean
- (x₁ × x₂ × … × xₙ)^(1/n), for positive values
How to read your statistics calculator result
Compare the mean and median: when the mean is much larger than the median, a few large values are pulling the average up. The IQR describes the spread of the middle half of the data and is less affected by outliers than the range.
Statistics Calculator worked example
The data 3, 7, 7, 9, 12, 15, 15, 15, 21, 30.
- n = 10, sum = 134, mean = 13.4.
- Median = (12 + 15) ÷ 2 = 13.5; mode = 15 (15 appears 3 times).
- Range = 30 − 3 = 27; Q1 = 7, Q3 = 15, IQR = 8.
- Sample standard deviation ≈ 7.8344.
Mean 13.4, median 13.5, mode 15.
Practical uses of the statistics calculator
- Summarising exam scores or sales figures.
- Checking for outliers with the quartiles.
- Producing the numbers for a report table.
Assumptions and limitations of this calculator
- Quartile methods differ between textbooks and software; the method used here is stated and may differ slightly from yours.
- Geometric and harmonic means require all values to be greater than zero.
- Up to 10,000 values.