Statistics Calculator (Mean, SD)

Statistics Measures Guide

Mean, Median, and Mode

Mean: sum of all values ÷ count. Sensitive to outliers — a single extreme value can significantly shift the mean. Median: the middle value when sorted. For even counts, the average of the two middle values. Much more resistant to outliers — the median income is more representative of typical earnings than mean income because a few extremely high earners pull the mean up significantly. Mode: the most frequently occurring value. Can be multiple (bimodal distribution) or none (all values unique). M

Standard Deviation

Standard deviation measures how spread out values are from the mean. A small SD means values cluster tightly around the mean. A large SD means high variability. Population SD divides by n; sample SD divides by n−1 (Bessel's correction — accounts for the fact that a sample underestimates population variance). Approximately 68% of values fall within 1 SD of the mean in a normal distribution, 95% within 2 SD, 99.7% within 3 SD (the empirical rule / 68-95-99.7 rule).

When to Use Which Measure

Mean: best for symmetrical distributions without outliers. Median: best for skewed distributions or data with outliers (income, house prices, response times). Mode: best for categorical data or finding the most common value. Use both mean and median when you have a dataset — if they differ significantly, you have a skewed distribution or outliers. For investment returns, the geometric mean (not arithmetic) is the correct measure of average compounding growth.

Five-Number Summary

The five-number summary (minimum, Q1, median, Q3, maximum) gives a comprehensive view of distribution shape. Q1 is the median of the lower half; Q3 is the median of the upper half. The interquartile range (IQR = Q3 − Q1) captures the middle 50% of data. Outliers are often defined as values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. Box plots visualise the five-number summary and are particularly useful for comparing distributions across groups.