Statistics Calculator with the working shown

Paste your numbers once and get every descriptive statistic your worksheet asks for, laid out step by step the way your teacher wants to see it. Then check anything else: z-scores, p-values, t-tests, sig figs, scientific notation.

9 values read.

Mean
14.5556
Median
15
Sample SD (s)
2.2973
Mode
15
Population SD (σ)
2.166
Sample variance
5.2778
Range
7
Min / Max
11 / 18
Count
9
Sum
131
Std error
0.7658
Q1 / Q3
12.5 / 16.5
IQR
4
Mean abs. deviation
1.8272
Coeff. of variation
15.78%
Skewness
−0.0916
Excess kurtosis
−0.8277
Geometric mean
14.3904
Harmonic mean
14.2224
±1 SD1112131415161718
▲ mean 14.5556 · ◆ median 15 · shaded band = mean ± 1 SD (12.2582 to 16.8529)

Step-by-step working

  1. Count the valuesn = 9
  2. Add the values and divide by the count to get the meanx̄ = (12 + 15 + 11 + 18 + 14 + 16 + 13 + 17 + …) ÷ 9 = 131 ÷ 9 = 14.555556
  3. Subtract the mean from each value, then square the result (see the table)(x − x̄)² for each x, e.g. (12 − 14.5556)² = 6.530864
  4. Add up the squared deviations (the sum of squares)SS = Σ(x − x̄)² = 42.222222
  5. Divide by n − 1 for the sample variance (Bessel’s correction)s² = 42.222222 ÷ 8 = 5.277778
  6. Take the square root to get the standard deviations = √5.277778 = 2.297341
Frequency table
ValueFrequencyRelativeCumulativeCum. %
1110.1111111.11%
1210.1111222.22%
1310.1111333.33%
1410.1111444.44%
1520.2222666.67%
1610.1111777.78%
1710.1111888.89%
1810.11119100%
Deviation table
xx − x̄(x − x̄)²
12−2.55566.5309
150.44440.1975
11−3.555612.642
183.444411.8642
14−0.55560.3086
161.44442.0864
13−1.55562.4198
172.44445.9753
150.44440.1975
Σx = 131≈ 0SS = 42.2222

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

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What standard deviation is actually measuring

Drag any dot (or focus it and use ← →). Each square’s side is that value’s distance from the mean, so its area is the squared deviation. Standard deviation is the side of the “average” square.

012345678910mean 5.17

Σ(x − x̄)² = 10.03 + 1.36 + 1.36 + 0.03 + 3.36 + 14.69 = 30.83
s = √(30.83 ÷ 5) = 2.48

Why n − 1? A sample’s values sit closer to their own mean than to the true population mean, so squared deviations from x̄ run slightly small. Dividing by one less (Bessel’s correction) makes the variance unbiased. Notice the difference shrinks as n grows.

Standard deviation clicks for most people the moment they see the squares change size as a point moves. The same visual approach drives ahaboo, where you can work through explainers like how US tax brackets really work, marginal versus effective rate.

How to use it for homework

  1. Paste or type your data in the box. Commas, spaces, tabs and line breaks all work.
  2. Read the highlighted results: mean, median and sample standard deviation are the three most assignments want.
  3. Copy the working. The numbered steps and the deviation table show every intermediate value, so you can compare them line by line with your own attempt and find exactly where a mistake crept in.
  4. Not sure what it means? Press “Explain my result” and the tutor will interpret your numbers in plain English.

Sample or population standard deviation?

This page reports both. Use the sample standard deviation (s, dividing by n − 1) when your data are a sample from a bigger group, which covers most homework, lab and survey data. Use the population value (σ, dividing by N) only when the list is the entire group you care about. The standard deviation calculator lets you switch between them and explains why n − 1 is used.

Frequently asked questions

What does this statistics calculator work out?

From one list of numbers (or a value–frequency table) it gives the count, sum, mean, median, mode, range, minimum and maximum, quartiles and IQR, sample and population standard deviation and variance, standard error, mean absolute deviation, coefficient of variation, skewness, excess kurtosis, and the geometric and harmonic means, plus a dot plot, a frequency table and the full working for the standard deviation.

Are the answers the same as my TI-84 or Excel?

Yes for mean, median, standard deviation and variance: sample SD matches Sx on a TI-84 and STDEV.S in Excel; population SD matches σx and STDEV.P. Quartiles follow the TI-84 method, and the quartile page notes when Excel’s method would differ.

Is it free, and do I need an account?

Every calculator is free with no sign-up. Calculations run in your browser. Your last inputs are remembered on your own device so a page refresh doesn’t lose your work; you can clear them on the privacy page.

Do I need a TI-84 for statistics?

Many courses and exams (AP Statistics, for example) let you use a graphing calculator, and a TI-84 is a common choice, but you do not need one to do homework. This site gives the same 1-Var Stats numbers (x̄, Sx, σx, the five-number summary) plus the working, which a TI-84 does not show. Check your exam rules before test day.

How do I calculate statistics by hand?

Sort the data, find the mean (sum ÷ count), median (middle value) and mode (most frequent), then for spread subtract the mean from each value, square, add and divide by n − 1 for the sample variance; its square root is the standard deviation. The step-by-step panel above does exactly this with your numbers.

Can I paste data from a spreadsheet?

Yes. Copy a column or row from Excel, Google Sheets or Numbers and paste it in. Commas, spaces, tabs and new lines all work as separators.