Core Focus on Linear Equations Lesson 5.3 Core Focus on Linear Equations Five-Number Summaries of Data

Warm-Up 1. What are the two characteristics of a good line of best fit? For #2-5, use the following data set: 33, 27, 33, 38, 43, 9, 28, 38, 30 2. What are the mean, median and mode of the data set? 3. Is there an outlier in the data set? Explain. 4. Which measure of center best describes the data set? Why? 5. What is the range of the data? The line follows the direction of the data well. Also, about half of the points should be above the line and about half should be below. Mean = 31, Median = 33, Mode = 33, 38 Yes, 9 is far lower than the other values. Median. There is an outlier and two modes, so the median would best describe the data. 34

Five-Number Summaries of Data Lesson 5.3 Five-Number Summaries of Data Find the five-number summary of data sets. Find the interquartile range (IQR) of data sets.

Vocabulary Five-Number Summary Describes the spread of the numbers in a data set. Median The middle number in an ordered data set. 1st Quartile (Q1) Median of the lower half of the data. 3rd Quartile (Q3) Median of the upper half of the data. Interquartile Range (IQR) The difference between the third quartile and first quartile in a set of data.

Minimum ~ Q1 ~ Median ~ Q3 ~ Maximum Five-Number Summary Minimum ~ Q1 ~ Median ~ Q3 ~ Maximum 1st Quartile 3rd Quartile

Good to Know! Finding the Five-Number Summary 1. Put the numbers in order and find the median. 2. Find the median of the lower half of the data. This is called the 1st Quartile. 3. Find the median of the upper half of the data. This is called the 3rd Quartile. 4. Identify the minimum and maximum values. You should also know…  DO NOT include the median in the upper or lower half!  The word “quartile” refers to how the data is separated into quarters.

Example 1 Find the five-number summary of the data set. 24, 29, 30, 35, 39, 43, 45, 48, 48, 50 Find the median of the data set. 24, 29, 30, 35, 39, 43, 45, 48, 48, 50 Find the 1st Quartile. If there are two numbers in the middle, include one in each half of the data. Find the 3rd Quartile. Find the minimum and maximum. The five-number summary is 24 ~ 30 ~ 41 ~ 48 ~ 50. Q1 41 median Q3

Example 2 Find the five-number summary of the data set. 9, 10, 7, 19, 17, 8, 20, 12, 23 Put the numbers in order. 7, 8, 9, 10, 12, 17, 19, 20, 23 Find the median of the data set. Find the 1st quartile. When there is an odd number of values in the data set, do not include the median in either half. Find the 3rd quartile. Find the minimum and maximum. The five-number summary is 7 ~ 8.5 ~ 12 ~ 19.5 ~ 23. 8.5 Q1 median 19.5 Q3

Interquartile Range The interquartile range (IQR) is the difference between the third quartile and the first quartile in a set of data. IQR = Q3 – Q1

Example 3 The following data lists the average points per game of players on the Miami Heat for the 2011-2012 season. (Source espn.com) 3.0, 3.0, 3.4, 3.6, 3.6, 4.8, 6.0, 6.1, 6.8, 9.8, 18.0, 22.1, 27.1 a. Find the five-number summary for the data set. The middle number of the data set (the median) is 6.0. The medians of the lower and upper halves, Q1 and Q3, are 3.5 and 13.9, respectively. The minimum is 3.0 and the maximum is 27.1. The five-number summary for the data is 3.0 ~ 3.5 ~ 6.0 ~ 13.9 ~ 27.1. 3.5 Q1 median 13.9 Q3

Example 3 Continued… The following data lists the average points per game of players on the Miami Heat for the 2011-2012 season. (Source espn.com) 3.0, 3.0, 3.4, 3.6, 3.6, 4.8, 6.0, 6.1, 6.8, 9.8, 18.0, 22.1, 27.1 b. Find the range and interquartile range of the average points per game by the players. Find the range of the data. Range = Maximum – Minimum = 27.1 – 3.0 = 24.1 Find the interquartile range. IQR = Q3 – Q1 = 13.9 – 3.5 = 10.4 3.5 Q1 median 13.9 Q3

Communication Prompt Given a data set, what steps should you take to find the interquartile range (IQR) of the data?

Exit Problems Find the five-number summary and IQR of the following data sets. 26, 34, 45, 33, 40, 44, 39 82, 87, 92, 97, 97, 98, 102, 109 26 ~ 33 ~ 39 ~ 44 ~ 45; IQR = 11 82 ~ 89.5 ~ 97 ~ 100 ~ 109; IQR = 10.5