Statistics Calculator (mean, median, std dev, quartiles)

What each statistic measures

Mean (average): sum divided by count. Sensitive to outliers — a single huge value can pull the mean far from the typical value. Best when data is roughly symmetric.

Median: the middle value when sorted. Robust to outliers — a few extreme values don't move it. Better than mean for skewed data like income or house prices.

Mode: the most frequent value. Most useful for discrete data (survey responses, dice rolls). For continuous data, mode is often meaningless and we report 'none' if no value repeats.

Standard deviation: typical distance from the mean. Same units as your data. Two-thirds of values typically fall within ±1 standard deviation of the mean (for normal distributions).

Sample vs population

If your numbers are the entire population (every employee in your company, every day of a month), use population standard deviation: divide by n. We toggle this off when you uncheck 'Sample standard deviation'.

If your numbers are a sample drawn from a larger population (a survey of 100 from 10,000 customers), use sample standard deviation: divide by n−1 (Bessel's correction). This is the default and is what most statistics courses and software default to.

The difference shrinks as n grows. For n=100 the two differ by 0.5%; for n=10 they differ by 5%. For very small samples, the choice matters.

Quartiles and the IQR

Q1 (first quartile, 25th percentile) is the median of the lower half. Q3 (third quartile, 75th percentile) is the median of the upper half. The interquartile range (IQR = Q3 − Q1) describes the middle 50% of your data and is robust to outliers.

Box plots use these: the box spans Q1 to Q3, with the median as a line inside. Whiskers extend to the most extreme values within 1.5 × IQR; anything beyond is plotted as outliers.