Statistics Calculator (Mean, SD)
Enter a list of numbers and instantly calculate all key statistics — mean, median, mode, range, variance, and standard deviation with full working shown.
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Statistics Measures Guide
What should I know about 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). Median is generally the more representative average for skewed data, such as income or house prices, where a small number of high values would otherwise distort the mean.
What's the key thing to understand about 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.
What do I need to know about 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.