Calculators

Statistics Calculator

Calculate mean, median, mode, standard deviation and more

Last reviewed: How we build & verify
Mean
0.0000
Median
0.0000
Mode
None
Std Deviation
0.0000
Variance
0.0000
Sum
0
Count
1
Range
0
Min / Max
0 / 0

Solution Steps

Pro feature
Formulasum = Σxᵢ, n = count
Substitutionsum = 0 = 0, n = 1
Result:sum = 0, n = 1

Add every value together and record the number of entries.

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Data Distribution

Frequency of values in the dataset

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What This Means For You

Get a personalized explanation of these results — what they actually mean for your situation, and how small changes would affect them.

How it works

Takes a list of numbers and returns the standard descriptive summary: mean, median, mode, range and standard deviation. Mean and median answer different questions, and the gap between them is a quick read on whether the data is skewed.

Formula
Mean x̄ = Σx / n
Median = middle value of the sorted list (average of the two middle values when n is even)
σ = √( Σ(xᵢ − x̄)² / n )   (population)
s = √( Σ(xᵢ − x̄)² / (n − 1) )   (sample)
Variables
  • ncount of values
  • x̄arithmetic mean
  • Modemost frequent value; undefined when every value appears once
  • Rangelargest value minus smallest
  • σ, spopulation and sample standard deviation
Worked example
Inputs: 12, 15, 15, 18, 22, 24, 30
  1. Sum = 136 over n = 7, so the mean is 136 / 7 = 19.43
  2. Already sorted; the 4th of 7 values is the median: 18
  3. 15 appears twice and every other value once, so the mode is 15
  4. Sum of squared deviations from the mean = 235.71
  5. Population: 235.71 / 7 = 33.67, so σ = 5.80
  6. Sample: 235.71 / 6 = 39.29, so s = 6.27
Result: Mean 19.43, median 18, mode 15, range 18, σ = 5.80 (s = 6.27)
Notes
  • This tool divides by n, giving the population standard deviation. If your numbers are a sample drawn from something larger, divide by n − 1 instead; on seven values that raises the figure by about 8%.
  • Mean above median, as here, points to a right tail. The value 30 drags the average up while leaving the median untouched, which is exactly why median income gets reported rather than mean income.
  • A dataset can have no mode, one mode, or several. Two distinct peaks usually means two populations got mixed together, and no single summary number will describe that honestly.

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Frequently Asked Questions

Mean is the arithmetic average. Median is the middle value when data is sorted. Mode is the most frequently occurring value. Each describes the center of a dataset differently.

Use the median when data is skewed or contains outliers. For example, median household income is more representative than mean income because very high earners skew the average.

Standard deviation measures how spread out values are from the mean. A low standard deviation means data points cluster near the average; a high one means they are more dispersed.

Population statistics describe an entire group, while sample statistics estimate population parameters from a subset. Sample standard deviation divides by (n-1) instead of n to correct for bias.

Statistics Calculator | ExaCalc