Descriptive Statistics Calculator

Summarizing observations

The mean is the sum divided by the observation count. The median is the middle of the sorted list. Modes are the most frequent values. All tied modes are reported. A list with no repeated values has no mode under this convention.

Spread and percentiles

Population variance divides the sum of squared deviations by n, while sample variance uses n − 1. Sample variance is undefined for a single observation. Quartiles and percentiles use linear interpolation at position h = (n − 1)p in the sorted list, starting at zero. Other percentile definitions may give different results. For the list 1, 2, 3, 4, the first quartile is 1.75. Missing values and outliers are never silently removed.

Do not read the mean alone

Use the list 1, 3, 3, 5, 8. Its sum is 20 and count is 5, so the mean is 4. The middle sorted value is median 3 and the most frequent value is mode 3. Squared deviations from the mean are 9, 1, 1, 1 and 16, totalling 28. Population variance is 28 / 5 = 5.6 and sample variance is 28 / 4 = 7. The first quartile is 3 and the third is 5.

Different variances for the same data do not indicate a calculation error. The denominator depends on whether the data describe the whole population or a sample from a larger group. Also distinguish units. Variance has squared measurement units, while standard deviation uses the original measurement unit.

Replacing a missing observation with zero changes both mean and spread. Distinguish real zero measurements from missing entries. Separate observations with spaces when using decimal commas to avoid separator ambiguity. Do not remove an outlier merely because it raises the mean. Inspect the record and measurement conditions first. These summaries alone establish neither normality nor causation.

Frequently asked questions

How do you calculate the mean, median and mode?

In this example, for the data list 2 4 4 6 9, the mean is 5, the median is 4 and the mode is 4. The mean divides the sum by the observation count, the median locates the middle and the mode identifies the most frequent value. Observations have equal weight, outliers are retained and these summaries alone do not establish representativeness.

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