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Mathematics · pattern F, Dataset

Mean, median and mode from your data.

Paste a column of numbers for all three averages plus the spread measures, with a chart marking the values that sit beyond one standard deviation.

Inputs

Sample or population

Divide by n − 1 for a sample drawn from a wider population; by n only when the data is the entire population.

The formula used

mean = Σx ÷ n; median is the middle value; mode is the most frequent

All three are averages and they answer different questions. Report the one that matches the shape of the data, and say which you used.

Mean

40.917

n = 12 · sample, ÷ (n − 1)

n
12
Sum
491.000
Mean
40.917
Median
39.500
Mode
35.000
Σ(x − x̄)²
1,410.917
Variance
128.265
Standard deviation
11.325
Standard error
3.2694
Minimum / maximum
23.00 / 61.00
Range
38.000
Q1 / Q3 / IQR
34.00 / 48.25 / 14.25

Your data — accent bars sit beyond one deviation

23.0061.00

Skew decides between mean and median.

For symmetric data the mean and median agree and either will do. For skewed data — incomes, house prices, response times — the mean is dragged toward the extremes while the median stays with the typical case, which is why official statistics report median income.

Questions about average

Which average should I use?
Median for skewed data, mean for symmetric data and for anything needing further arithmetic, mode for categories.
Can data have two modes?
Yes. Bimodal data usually means two populations have been combined.
What is a weighted mean?
An average where values carry different weights, such as a GPA. It divides by the sum of the weights rather than the count.

More in Mathematics

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A calculator handles the arithmetic. It cannot teach you the method.

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Arithmetic runs in double-precision floating point, so results beyond about fifteen significant figures are not exact. Where a question wants an exact fraction or surd, keep the exact form rather than a decimal.