Standard Deviation Calculator
Calculate the complete statistical summary of any data set — mean, median, mode, range, variance, and standard deviation. Essential for statistics coursework and data analysis.
Population vs Sample Std Dev
Population std dev (σ) divides by n — use when you have all the data. Sample std dev (s) divides by n−1 — use when your data is a sample from a larger population. For most coursework and experiments, you want the sample standard deviation.
What Standard Deviation Tells You
Std dev measures spread around the mean. Low std dev = data clustered near the mean. High std dev = data spread widely. In a normal distribution, 68% of data falls within 1 std dev of the mean, 95% within 2, and 99.7% within 3 (the empirical rule).
When to Use Which Average
Mean: symmetric data without outliers. Median: skewed data or outliers present (house prices, salaries). Mode: categorical data or finding the most common value. For exam scores: mean shows average performance; median shows what the 'typical' student scored.
Exam Tips and Common Errors
Common mathematical errors to avoid: sign errors when moving terms across an equation (changing sign), order of operations (BIDMAS/BODMAS — brackets, indices, division and multiplication, addition and subtraction), not checking whether answers are reasonable (a negative length or probability outside 0-1 indicates an error), and rounding too early in multi-step calculations (carry extra decimal places until the final step). Always substitute your answer back into the original equation or problem
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