Core Focus on Ratios, Rates & Statistics Measures of Center Lesson 4.2

Evaluate Put the following numbers in order: Warm-Up 13 11

Measures of Center Find measures of center and range. Lesson 4.2

Vocabulary Measures of Center Three numbers which are commonly used to represent a set of numbers. (Mean, Median and Mode) Mean The sum of all the values in a data set divided by the number of values; also known as an average. Median When all the numbers have been put in order from least to greatest, the median is the middle number of the ordered data set. Mode The number(s) or item(s) in a data set which occurs the most often.

The measures of center can be used to summarize the number of pets that students own. Cameron asked eight of his classmates how many pets they own. The results are listed below. 1, 0, 2, 0, 3, 7, 0, 2 Step 1 Cameron wants to know the average number of pets that students own. The word “average” refers to the mean of the data set. The mean is the sum of all the values divided by the number of values. a. Find the sum of all the pets in the list. b. Divide the sum by the number of students Cameron asked. This number represents the mean of the data.

Step 2 Another measure of center is called the median. When all the numbers have been put in order from least to greatest, the median is the middle number of the ordered data set. a.Put the numbers in Cameron’s list in order from least to greatest. b.Because there are an even number of values in the data set, there will be two middle numbers in the list. Count in from each end to find the two middle numbers. What are they? c. When there are two middle numbers, the median is found by finding the mean of the two middle numbers. Add the two middle numbers together and divide by two. This is the median.

Step 3 The last measure of center is the mode. The mode is the number(s) or item(s) in a data set which occurs the most often. There can be one mode, no mode or multiple modes. What number of pets showed up most often in Cameron’s data set? This is the mode. Step 4 If Cameron wants to convince his parents that they should get another pet, which measure of center should he use? Explain your choice.

Measures of Center Mean The sum of all values divided by the number of values Median The middle number of an ordered data set If there are two middle numbers, find the mean of those numbers. Mode The number or item in a data set which appears most often A data set may have one mode, no mode or several modes.

Example 1 Find the mean, median and mode for the following data sets: a.3, 8, 9, 9, 10, 10, 28 Find the mean. The mean is 11. Find the median.3, 8, 9, 9, 10, 10, 28 The median is 9. Find the mode.Both 9 and 10 appear twice. The modes are 9 and 10. Total numerator before dividing.

Example 1 Continued… Find the mean, median and mode for the following data sets: b.17, 8, 10, 15, 19, 2, 9, 12 Find the mean. The mean is Find the median. Order2, 8, 9, 10, 12, 15, 17, 19 the numbers from least to greatest. Ten and twelve are the middle numbers. Find the mean of these numbers. The median is 11. Find the mode.No number appears more There is no mode.than any other number.

Vocabulary Range The difference between the maximum (largest value) and minimum (smallest value) values in a data set.

Range = Maximum - Minimum The maximum is the largest number in the data set. The minimum is the smallest number in the data set.

Example 2 Find the range of the following data sets. a. 17, 29, 33, 34, 38, 42 b. 26, 37, 40, 33, 35, 38 a. The maximum is 42 and the minimum is 17. Range= Maximum − Minimum = 42 − 17 = 25 b. The maximum is 40 and the minimum is 26. Range= Maximum − Minimum = 40 − 26 = 14

Example 3 Use the range to find the missing value in each ordered data set. a. 11, 13, 16, 20, 22, ___ Range = 19 The range is 19 and theRange = Maximum – Minimum minimum is = Maximum – 11 Add 19 to 11 to find the = 30 maximum value. The missing value is 30. Think: What number minus 11 is 19?

Example 3 Continued… Use the range to find the missing value in each ordered data set. b. ___, 35, 40, 40, 41, 45, 52 Range = 25 The range is 25 and theRange = Maximum – Minimum maximum is = 52 – Minimum Subtract 25 from 52 to find 52 – 25 = 27 the minimum value. The missing value is 27. Think: 52 minus what number is 25?

Communication Prompt Which measure of center do you think is the easiest to find? Which is the most difficult to find? Explain.

Exit Problems 1.Find the mean, median and mode of the following data set. 20, 32, 24, 40, 24, 28 2.Give an example of a data set with more than one mode. 3. What is the range of the data set? 82, 77, 85, 92, 89, 99, 79, 85 Mean = 28; median = 26; mode = 24 0, 1, 3, 3, 4, 5, 6, 6, 7 22