Standard Deviation Calculator

Formula first

Overview

In geography, this formula quantifies the spread of data points, such as rainfall totals or migration rates, relative to the average. Using n-1 in the denominator indicates that this is a sample standard deviation, providing an unbiased estimate for a larger population.

Symbols

Variables

s = Sample Standard Deviation, $x_i$ = Individual data value, $\bar{x}$ = Mean of the sample, n = Sample size

Apply it well

When To Use

When to use: Use when you need to understand how consistent or varied a dataset is, specifically for sample data rather than an entire population.

Why it matters: It helps geographers differentiate between datasets that might have the same average but completely different underlying characteristics, such as stable vs. volatile climate patterns.

Avoid these traps

Common Mistakes

• Using n instead of n-1, which is only for population standard deviation.
• Forgetting to square the differences (x - mean) before summing them.
• Calculating the mean of the squared differences instead of dividing by n-1.

One free problem

Practice Problem

Calculate the standard deviation for the sample rainfall data (in mm): 10, 12, 14, 16. Round to one decimal place.

Solve for: $s$

Hint: Calculate the mean first (13), find the squared difference for each value, sum them, divide by (n-1=3), and take the square root.

The full worked solution stays in the interactive walkthrough.

References

Sources

1. Clark, W.A.V. and Hosking, P.L. (1986). Statistical Methods for Geographers.
2. AQA/Edexcel A-Level Geography Quantitative Skills Specification