## Standard and Absolute Deviation

#### Aligned To Common Core Standard:

**High School Statistics** - HSS-ID.A.2

What is the Difference Between Standard and Absolute Deviation? Measuring data sets is an essential part of handling a large number of data. There are different mathematical tools which you can use to measure data sets differently. Standard deviation and absolute deviation are one of the most used tools. Standard deviation is the most common tool for variability. It is found by finding the mean of the data points and subtracting them from each point and square the answer. Now you need to find the average of the squared differences by the total values minus 1. On the other hand, the absolute deviation is another measure of variability. However, it uses absolute values instead of squares. To calculate the average deviation, we subtract the mean from all data points, then we add the average absolute values of those differences. Standard deviation can be used to create strategies for investing and to help measure the market's performance trends, However, absolute deviation uses absolute values which makes the manipulation of different data sets more complicated. These worksheets and lessons help students understand the meaning and how to calculate standard and absolute deviations from data sets.

### Printable Worksheets And Lessons

- Mean Absolute Deviation Step-by-step Lesson- I made sure to give you a very light data set and baby step you through the process.
- Guided Lesson - We throw some units of measure in there and ask for the standard, variance, and mean.
- Guided Lesson Explanation - We walk through all the different formulas here.
- Practice Worksheet - Time to pound away at some data sets.
- Matching Worksheet - In this we round to the nearest thousandths, although the significant figures only dictate two digits.

#### Homework Sheets

Two sheets on mean deviation and a final sheet on standard deviation.

- Homework 1 - First add all of the numbers in the data set together. Then divide by the total number of values in the data set.
- Homework 2 - Take each number in the data set, subtract the mean and take absolute value. Then take the sum of the absolute values.
- Homework 3 -

#### Practice Worksheets

I made sure that the data sets were very compact here so that students could focus on the process rather than the math.

- Practice 1 - In the data set below, what is the mean absolute deviation? 55, 68, 78, 69, 43, 50, 40
- Practice 2 - Compute the mean absolute deviation by dividing the sum above by the total number of values in the data set.
- Practice 3 - Compute the mean, variance, and standard deviation.

#### Math Skill Quizzes

The quizzes follow the standard 6 to 9 pieces of data that you will find on most assessments.