Which standard deviation does this calculator use?

It uses the sample standard deviation, dividing the summed squared deviations by N − 1. If you specifically need the population standard deviation (divided by N) or want to switch between the two, use the dedicated standard deviation calculator.

How is the mode reported when there is no single most common value?

The calculator returns every value that ties for the highest frequency. If all values appear exactly once, all of them are returned as modes, which signals that the data set effectively has no distinct mode.

What is the difference between mean and median?

The mean is the arithmetic average and is pulled toward extreme values, while the median is the middle value when the data is sorted and resists outliers. Comparing the two is a quick way to spot skew in your data.

How does this compare to the mean, median, mode, and range calculator?

This calculator adds spread measures — standard deviation and variance — plus sum, count, minimum, and maximum on top of the central-tendency basics. The mean-median-mode-range tool covers only those four core measures.

Statistics Calculator

Dataset (comma-separated)

Mean5.0000

Median5.0000

Mode5

Range8.0000

Std Dev2.4495

Variance6.0000

Sum50.0000

Count10

Min1.0000

Max9.0000

This statistics calculator summarises a data set with one pass, returning the full set of descriptive measures: mean, median, mode, range, sample standard deviation, variance, sum, count, minimum, and maximum. It is built for quickly profiling a list of numbers without setting up a spreadsheet, whether for homework, lab data, or business metrics.

Formula

mean = Σxᵢ / N ; range = max − min ; s = √( Σ(xᵢ − x̄)² / (N − 1) )

xᵢ: Each value in the data set
N: The count of values
x̄: The mean of the data set
s: Sample standard deviation (variance uses the N − 1 divisor)

How it works

Enter your list of numbers; the calculator sorts a copy to find the median, minimum, and maximum without altering your input order.
It computes the mean (sum ÷ count), the median (middle value or average of the two middle values), and the mode (the most frequent value or values).
Spread measures use the sample formulas: variance divides the summed squared deviations by N − 1, and standard deviation is its square root. With fewer than two values, standard deviation and variance are reported as 0.

Worked example

Summarise the data set 4, 8, 15, 16, 16, 42.

Sum = 101, count = 6, so mean = 101 / 6 ≈ 16.83.
Sorted, the two middle values are 15 and 16, so median = 15.5; the mode is 16 (it appears twice); range = 42 − 4 = 38.
Sample variance ≈ 146.81 and sample standard deviation ≈ 12.12.

Mean ≈ 16.83, median 15.5, mode 16, range 38, SD ≈ 12.12, min 4, max 42

Frequently asked questions

Which standard deviation does this calculator use?: It uses the sample standard deviation, dividing the summed squared deviations by N − 1. If you specifically need the population standard deviation (divided by N) or want to switch between the two, use the dedicated standard deviation calculator.
How is the mode reported when there is no single most common value?: The calculator returns every value that ties for the highest frequency. If all values appear exactly once, all of them are returned as modes, which signals that the data set effectively has no distinct mode.
What is the difference between mean and median?: The mean is the arithmetic average and is pulled toward extreme values, while the median is the middle value when the data is sorted and resists outliers. Comparing the two is a quick way to spot skew in your data.
How does this compare to the mean, median, mode, and range calculator?: This calculator adds spread measures — standard deviation and variance — plus sum, count, minimum, and maximum on top of the central-tendency basics. The mean-median-mode-range tool covers only those four core measures.

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Mean Median Mode Range Calculator Standard Deviation Calculator Average Calculator Z-Score Calculator