# 5.17 - Measures of Center

The student, given a practical context, will

a) describe mean, median, and mode as measures of center;

b) describe mean as fair share;

c) describe the range of a set of data as a measure of spread; and

d) determine the mean, median, mode, and range of a set of data.

### BIG IDEAS

• So that I can use the mean when finding a player’s batting average
• So that I can analyze weather data using mean, median, range, and mode
• So that I can calculate my Math grade for the quarter
• So that when I get offered a job I can calculate my average salary
• So that I can look at the range in salaries for the same position in different locations to help decide where I should live
• So that I can look at the range in temperature for the day and choose the right attire

### UNDERSTANDING THE STANDARD

• Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.
• Students need to learn more than how to identify the mean, median, mode, and range of a set of data. They need to build an understanding of what the measure tells them about the data, and see those values in the context of other characteristics of the data in order to best describe the results.
• A measure of center is a value at the center or middle of a data set.  Mean, median, and mode are measures of center.
• The mean, median, and mode are three of the various ways that data can be analyzed.
• The mean, median, and mode are referred to as types of averages. The term arithmetic average can be used when referring to the mean.
• Mean represents a fair share concept of the data.  Dividing the data constitutes a fair share.  This idea of dividing as sharing equally should be demonstrated visually and with manipulatives to develop the foundation for the arithmetic process. The arithmetic way is to add all of the data points and then divide by the number of data points to determine the arithmetic average or mean.
• The median is the middle value of a data set in ranked order.  Given an odd number of pieces of data, the median is the middle value in ranked order.  If there is an even number of pieces of data, the median is the arithmetic average of the two middle values.
• The mode is the piece of data that occurs most frequently in the data set. There may be one, more than one, or no mode in a data set. Students should order the data from least to greatest so they can better determine the mode.
• The range is the spread of a set of data. The range of a set of data is the difference between the greatest and least values in the data set.  It is determined by subtracting the least number in the data set from the greatest number in the data set.  An example is ordering test scores from least to greatest:  73, 77, 84, 87, 89, 91, 94.  The greatest score in the data set is 94 and the least score is 73, so the least score is subtracted from the greatest score or 94 - 73 = 21.  The range of these test scores is 21.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Describe and determine the mean of a group of numbers representing data from a given context as a measure of center. (a, d)
• Describe and determine the median of a group of numbers representing data from a given context as a measure of center. (a, d)
• Describe and determine the mode of a group of numbers representing data from a given context as a measure of center. (a, d)
• Describe mean as fair share. (b)
• Describe and determine the range of a group of numbers representing data from a given context as a measure of spread. (c, d)

### KEY VOCABULARY

Updated: Mar 06, 2019