descriptive
Calculate the arithmetic mean (average) of a data set.
This is the worked example that ships with the calculator. Replace the values above with your own and press Calculate.
Formulax̄ = Σxᵢ / nn = 5
15.0000
3.0000
Free reference
Descriptive statistics summarise a data set with a few numbers: where the values center, how far they spread, and how they are positioned. These are the formulas the calculators on this page apply.
xbar = sum(x_i) / n - The arithmetic average of a data set.s^2 = sum((x_i - xbar)^2) / (n - 1) - Average squared distance from the sample mean with Bessel correction.s = sqrt(s^2) - The square root of the sample variance, back in the original units of the data.Six students score 4, 8, 6, 5, 3 and 7 on a ten-point quiz. Treating these six scores as a sample, find the sample standard deviation.
Inputs. Data: 4, 8, 6, 5, 3, 7. Type: sample (divide by n - 1).
s² = Σ(xᵢ - x̄)² / (n - 1) gives n = 6, x̄ = 5.5000Σ(xᵢ - 5.5000)² gives 17.500017.5000 / 5 gives 3.5000s² = 3.5000s = √s² √3.5000 gives 1.8708Answer: 1.8708
A typical score sits about 1.87 points from the mean of 5.5, so the quiz results are moderately spread out.
The sample version divides the sum of squared deviations by n - 1 (the Bessel correction), while the population version divides by n. Use the sample formula whenever your data are a sample drawn from a larger population, which is the usual case in coursework.
Use the median when the data are skewed or contain outliers. The mean uses every value, so one extreme observation can pull it far from the bulk of the data, while the median only depends on the middle of the ordered list.
It is the typical distance of an observation from the mean, expressed in the same units as the data. In the worked example above, scores typically fall about 1.87 points from the mean quiz score of 5.5.