# Concept check: Standard deviation

Six questions that will help you understand standard deviation more deeply.

## Introduction

The questions below are designed to help you think deeply about standard deviation and its formula.

Unlike most questions on Khan Academy, some of these questions aren't graded by a computer. You'll learn the most if you try answering each question yourself before clicking "explain".

## The formula (for reference)

The formula for standard deviation (SD) is

where means "sum of", is a value in the data set, $\bar{x}$ is the mean of the data set, and is the number of values in the data set.

## Part 1

**How can we see this in the formula for standard deviation?**

## Part 2

**If it is possible, do it! Can you create two different data sets? How about three?**

## Part 3

**Why or why not?**

*Hint: Think about the formula.*

## Part 4

Standard deviation is a measure of spread of a data distribution.

**What do you think**

*deviation*means?### Part 5

Here are the formulas for standard deviation (SD) and the formula for mean absolute deviation (MAD), both of which are measures of spread:

**What are the similarities between the formulas? What are the differences?**

### Part 6

Here's the formula that we've been using to calculate standard deviation:

Here's the formula that statisticians actually use:

**Are the two formulas equivalent?**