Statistics and Probability / Transforming Data

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.