# Statistics and Probability / Transforming Data

Activity 10 of 24
In this lesson, students investigate what happens to the summary measures for the distribution of a set of data when a constant is added to each data element or when each element is multiplied by a non-zero constant.

## Planning and Resources

Objectives
Students recognize how common data transformations affect measures of center and spread.

Vocabulary
transformation
distribution
mean
median
interquartile range (IQR)

Standard:

## Lesson Snapshot

#### Understanding

Adding (subtracting) a common value to each element of a data set will shift the center by that value, but will not change the measure of spread.

### What to look for

Transforming data is a fundamental process in data analysis through which unwieldy data can be transformed by shifting or scaling to assist in its analysis.

### Sample Assessment

One of the problems on a mathematics test was incorrectly stated. The teacher decided to add 3 bonus points to everyone's test score. If the mean grade on the test was originally 84 with a mean absolute deviation (MAD) of 10, what would the new mean and MAD be?

Answer: The mean would be 87 and the MAD would be 10.

#### The Big Idea

Students discover what changes occur in the measures of center and spread, when a data set is transformed by shifting or scaling.

### What are the students doing?

Students make conjectures about what will happen to a distribution when certain transformations are applied.

### What is the teacher doing?

Remind students to think about the mean as the balance point of a distribution.