Main content

## Praxis Core Math

### Unit 1: Lesson 3

Statistics and probability- Data representations | Lesson
- Data representations | Worked example
- Center and spread | Lesson
- Center and spread | Worked example
- Random sampling | Lesson
- Random sampling | Worked example
- Scatterplots | Lesson
- Scatterplots | Worked example
- Interpreting linear models | Lesson
- Interpreting linear models | Worked example
- Correlation and Causation | Lesson
- Correlation and causation | Worked example
- Probability | Lesson
- Probability | Worked example

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Center and spread | Lesson

## What are the center and spread of a data set?

A set of quantitative data with varying values may be shown as a list or a data display.

Suppose Pedro asks 7 friends how many pairs of shoes they own. Pedro can report his findings as a list or a data display such as a dotplot where each dot represents one response.

- List: 1, comma, 2, comma, 4, comma, 4, comma, 7, comma, 8, comma, 8

- Dotplot:

**Center**and

**spread**are ways to describe data sets like this.

- Center describes a
*typical value*of a data point. Two measures of center are mean and median. - Spread describes the
*variation*of the data. Two measures of spread are range and standard deviation.

### What skills are tested?

- Calculating the mean, median, and range from a list of values or a data display
- Comparing the mean, median, range, and standard deviation of data sets.
*You won't be tested on the formula for standard deviation.*

## How is the mean calculated?

The

**mean**is useful for describing the center of data with*similar*values.The mean is the average value.

## How is the median calculated?

The

**median**is useful to describe the center of data with .The median is the middle value

*when the data are ordered from least to greatest*.- If the number of values is odd, the median is the middle value.
- If the number of values is even, the median is the
*average*of the two middle values.

## How is the range calculated?

**Range**measures the

*total spread*of the data.

The range is the difference between the highest and lowest values.

A larger range indicates a greater spread in the data.

## How is standard deviation used ?

**Standard deviation**measures the

*typical spread*from the mean.

Standard deviation is the average distance between the mean and a data point.

Larger values of standard deviation indicate greater spread in the data.

## Your turn!

## Things to remember

Center describes a

*typical value*.**Mean**: Average value

**Median**: Middle value when data ordered from least to greatest

Spread describes the

*variation*of the data.**Range**: Total spread

**Standard deviation**: Average distance between the mean and a data point

## Want to join the conversation?

- gaergargasfgacvxbcxbxvbdgbdrtgbfgse srgsergerce e ge(3 votes)
- yes isnt that what we all feel(3 votes)

- What about the mode in things to remember? Is that not a typical question on the Praxis?(1 vote)
- qwertyuiopasdfghjklzxcvbnm(1 vote)