HesapHanem

Statistics Calculator (Mean, Median…)

How do I find mean and standard deviation?

Result

16.57
15.00
8.00
11.93
12.88
4.00
42.00
38.00
7
116.00

How it is calculated

Paste or type numbers separated by commas, spaces or line breaks; anything that is not a number is skipped. With n values xi the tool computes: sum = Σxi; mean = sum ÷ n; the median is the middle value after sorting (the average of the two middle values when n is even); the mode is the most frequent value (every value is listed, separated by commas, if several tie for the highest count, and "No mode" is shown when each value appears once); range = max − min; and two standard deviations: the population standard deviation σ = √(Σ(xi − mean)² ÷ n) and the sample standard deviation s = √(Σ(xi − mean)² ÷ (n − 1)), which is undefined for a single value. Results are rounded to two decimals.

Worked example

Data: 4, 8, 15, 16, 23, 42, 8. Count = 7 and sum = 116, so mean = 116 ÷ 7 = 16.57. Sorted: 4, 8, 8, 15, 16, 23, 42; the middle (4th) value gives median 15. The value 8 appears twice, so mode = 8. Range = 42 − 4 = 38. The squared deviations sum to about 995.7; divided by 7 and square-rooted that gives a population standard deviation of 11.93, and divided by 6 instead a sample standard deviation of 12.88. The tool lists count 7 first.

Try this example →

Common mistakes

  • Using the population standard deviation when you have a sample. The first figure divides by n; for a sample estimate use the sample standard deviation, which divides by n − 1 and is slightly larger.
  • Typing a decimal comma in lists such as "3,5, 4,2". Commas separate numbers here, so 3,5 becomes the two numbers 3 and 5. Use a decimal point.
  • Forgetting that a typo is silently dropped. A word or stray symbol is skipped rather than flagged, so check that the count matches the number of values you meant to enter.
  • Expecting a mode when no value repeats. The tool shows "No mode" in that case; when several values tie, it lists all of them.
  • Taking the mean as typical for skewed data. In the example the mean (16.57) is above the median (15) because of the large value 42.

Sources

About this calculator

This calculator takes a list of numbers you enter and returns the core descriptive statistics in one pass: the mean (average), median (middle value), mode (most frequent value), minimum and maximum, range, and standard deviation (population and sample) — the measure of how spread out the values are around the average.

It is used by students checking homework or exam-prep problems, researchers and analysts getting a quick summary of a small dataset without opening a spreadsheet, and anyone — from a teacher averaging test scores to a small business owner looking at sales figures — who needs a fast statistical snapshot of a handful of numbers.

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Comments (1)

  • Editorial team

    Use the standard deviation as a yardstick for single values. For roughly bell-shaped data, about two thirds of the values sit within one standard deviation of the mean, so a score far outside that band deserves a second look. Because this tool divides by n, it suits a complete group such as every score in one class. When one extreme value drags the mean away from the median, quote the median alongside it. What kind of data do you usually paste in?

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