## Data and Statistics

**Statistics**

Statistics is the field of mathematics that provides ways of analyzing and making sense of data. When analyzing data, there are three useful measures of central tendency. These are the **mean,** the **median,** and the **mode.** Each describes the data in a different way.

Example:

Suppose 9 children practice their music lessons the following numbers of hours in a given week.

2, 2, 2, 2, 3, 4, 4, 4, 13

How much did a typical child practice? There are three ways to answer this question. Each is correct.

**Mean**

The mean, or average, of the data is the sum divided by the total number of entries.

Mean: (2 + 2 + 2 + 2 + 3 + 4 + 4 + 4 + 13) ÷ 9 = 4

Four hours is a good measure for a typical child because if each child practiced for 4 hours, the total number of hours practiced would be the same.

**Median**

The median of the data is the number in the middle when the numbers are arranged in increasing order. When there is an even number of data entries, the median is the sum of the two middle numbers divided by two.

The median is 3 hours. Three hours is a good measure for a typical child because four children practiced for more than 3 hours and four children practiced for less than 3 hours.

**Mode**

The mode is the number that appears most often in the data set. Sometimes there is more than one mode. Sometimes there is no mode.

The number 2 appears most often, so 2 is the mode. Two hours is a good measure for a typical child because more children practiced for 2 hours than any other amount of time.

Identifying the range of the data as well as clusters, gaps, and outliers is also useful in analyzing data.

**Range**

The range of the data is the difference between the greatest and the least values in a data set. The range tells how spread out the data are.

Range 13 − 2 = 11

Line plots are another way of organizing data. The mean, median, and mode can be identified from a line plot. Line graphs can also be used to display data.

**Teaching Model 8.4:** Make a Table