Activities & Lessons

# Grades 9-12 Math Activity Set 4: Measures of Central Tendency and More

This week’s lessons are about measures of central tendency and dispersion, outliers, transformations of data, and sampling techniques.

## Materials Needed

Each lesson has an answer sheet that provides guidance, a description of the key concept, and questions from the lesson. Use this sheet to check your answers.

The student sheet can be printed and completed by the student, or the student can write the answers on a blank sheet of paper.

You will also need:

• Paper
• Pencil
• Graphing calculator

### Activity 1: Measures of Central Tendency

“What is a typical value for the data set?”

Use this lesson to learn how measures of central tendency, also known as measures of location, can provide an answer to the question.

The three most common measures of central tendency are the mean, median, and mode. In addition to finding these measures, you will learn to choose the measure that is most appropriate in a given situation.

### Activity 2: Measures of Dispersion

In the last lesson, you learned how to describe a data set with a single value using measures of central tendency. While these measures give a sense of a “typical” data value, they do not describe how the data are spread out.

Use this lesson to learn how to calculate several measures of dispersion, including the range, the interquartile range, the variance, and the standard deviation.

### Activity 3: Outliers

In general terms, an outlier is simply a data value that is significantly different from the rest of the data. There are various criteria for establishing mathematically whether a particular value is an outlier.

Use this lesson to learn two tests for determining whether a data set contains outliers. As you learn, consider the effect that outliers have on measures of central tendency and on data displays.

### Activity 4: Transformations of Data

A transformation of a data set is a function that changes the values in the set.

Use this lesson to explore additive and multiplicative transformations and examine the effect of such transformations on measures of central tendency and measures of dispersion.

### Activity 5: Sampling Techniques

To understand sampling and surveys, it is important to understand the essential vocabulary for identifying different types of samples.

Use this lesson to learn more about the vocabulary of sampling and surveys. You will also learn to examine the benefits of random samples and to analyze survey results for possible sources of bias.