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📘 Lesson 6 of 11 · Statistics

📏 Standard Deviation

Standard deviation is the square root of variance — it measures spread in the same units as the original data, making it much easier to interpret directly.

Course progress: 55%

01 Key Concepts

Definition

Standard deviation = square root of variance. It tells you the 'typical' distance of data points from the mean.

Population vs. Sample Standard Deviation

Population standard deviation (sigma) is the square root of population variance; sample standard deviation (s) is the square root of sample variance.

Interpreting Standard Deviation

A small standard deviation means data points are close to the mean; a large one means they're spread out.

Relationship to the Normal Distribution

In a normal distribution, about 68% of data falls within 1 standard deviation of the mean, and about 95% within 2 (the Empirical Rule).

Comparing Datasets

Standard deviation lets you compare the consistency of two datasets even if they have the same mean — the one with the smaller standard deviation is more consistent.

02 Key Formulas

03 Solved Examples

Example 1 Find the population standard deviation of 2, 4, 6, 8 (population variance was found to be 5).
  1. Standard deviation = square root of variance = sqrt(5).
Answer: Approximately 2.24
Example 2 Two classes have the same mean test score of 75. Class A has standard deviation 5, Class B has standard deviation 15. Which class has more consistent scores?
  1. A smaller standard deviation indicates scores are closer to the mean, i.e., more consistent.
  2. Class A's standard deviation (5) is smaller than Class B's (15).
Answer: Class A has more consistent scores
Example 3 If a dataset has standard deviation 0, what does that tell you?
  1. A standard deviation of 0 means there is no spread at all.
  2. Every value in the dataset must be identical, equal to the mean.
Answer: All values in the dataset are exactly equal to the mean

04 Practice Questions

1Find the standard deviation of a dataset with variance 16.
4
2Find the standard deviation of a dataset with variance 100.
10
3If variance = 0, find the standard deviation.
0
4Which class is more consistent: A (std dev 8) or B (std dev 3)?
Class B
5What is standard deviation the square root of?
Variance

📄 Standard Deviation — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet