Statistics Calculator: Mean, Median, Mode & Range (Datasets)
Calculate all basic descriptive statistics for any dataset: mean, median, mode, range, variance, and standard deviation.
Descriptive Statistics Guide
Mean, Median, Mode
Mean: sum of all values / number of values. Sensitive to outliers. Best for symmetrical, normally distributed data. Median: middle value when sorted. Odd n: middle value. Even n: average of two middle values. Resistant to outliers. Best for skewed data (house prices, incomes). Mode: most frequently occurring value. Can have multiple modes (bimodal) or none (all values unique). Best for categorical data. Range: maximum − minimum. Interquartile range (IQR): Q3 − Q1 (middle 50% of data). More robus
Standard Deviation
Variance σ² = Σ(x − x̄)² / n. Population variance (divide by n). Sample variance (divide by n−1) — unbiased estimate. Standard deviation σ = √variance. Interpretation: approximately 68% of data within 1σ of mean. 95% within 2σ. 99.7% within 3σ (if normally distributed). Example: data 2, 4, 4, 4, 5, 5, 7, 9. Mean = 5. Deviations: −3, −1, −1, −1, 0, 0, 2, 4. Squared: 9,1,1,1,0,0,4,16. Sum: 32. Variance = 32/8 = 4. SD = 2. Coefficient of variation: σ/x̄ — useful for comparing spread of datasets wit
When to Use Which Average
Mean: test scores (normally distributed, no outliers). Average speed on a journey. Temperature readings. Median: house prices (skewed by luxury properties). Salary data (skewed by very high earners). Any data with significant outliers. Mode: shoe size sales (which size to stock most). Most popular choice from a survey. Favourite colour, most common grade. Comparing measures: if mean > median: right-skewed distribution (few high values pulling mean up). If mean < median: left-skewed. If mean ≈ me
GCSE Statistics Exam Tips
Interpreting spread: standard deviation is more informative than range because it uses all data points. IQR ignores outliers (uses middle 50%). Box plots: display min, Q1, median, Q3, max. Outliers: typically defined as values more than 1.5 × IQR below Q1 or above Q3. Comparing two datasets: use the mean (or median) to compare average performance. Use standard deviation (or IQR) to compare consistency. Example: class A mean 65%, SD 5. Class B mean 65%, SD 15. Same average but B has much more spr
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