Interquartile Range as a Measure of Variation

Launch – Review Turn and Talk (30 sec) number of toppings students like When we analyze data, what are we looking for? Median Center Mean Range Today! Spread (Measure of Variation) Interquartile Range Mean Absolute Deviation Shape

Launch Think-Pair-Share Test Scores: Would you expect a wide or narrow range? Twenty students take a social studies test. The range of the scores is 98 points. The teacher is worried that there is such a wide range of scores. How do you think the students performed?

Launch Whole Class The test scores are below. 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 How do you think the students performed?

Launch Whole Class In this example, was the range a useful measure of variation to use to determine how a class of students performed? NO!!

Explore Turn and Talk inter quartile Since the range is greatly influenced by outliers, we also use the interquartile range (IQR) to describe the variability of a data set. Are there any parts of the word interquartile that look familiar to you? inter quartile Between Quarters

Explore Notes Quartiles: the points that divide a data set into roughly four equally-sized parts To divide the data set into fourths: 1) Find the median 64° 60° 62° 67° 59° 62° 59° 70° 66° 70° 62° 62° 67° 65° 80° 59° 60° 62° 64° 65° 66° 67° 70° 80° median 7 7

Explore Whole Class Now that we have found the median (64°), how many equal parts do we have? Two roughly equal parts! What should we do next to break our data set into quartiles? Break the two parts we have in half to make four parts! Remember that quartiles are the points that divide a data set into roughly four equally-sized parts! 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° median 8 8

Explore Notes Quartiles: the points that divide a data set into roughly four equally-sized parts To divide the data set into fourths: Find the median Find the lower quartile (Q1): the median of all values below the median 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° lower quartile (Q1) 9 9

Explore Notes Quartiles: the points that divide a data set into roughly four equally-sized parts To divide the data set into fourths: Find the median Find the lower quartile (Q1): the median of all values below the median Find the upper quartile (Q3): the median of all values above the median 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° upper quartile (Q3) 10 10

Explore Check Your Work! median upper quartile (Q3) lower quartile (Q1) 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° 11

Explore Independent 1. Quartiles divide a data set into roughly four equally-sized parts. How could this be illustrated in the figure below? 2. What percentage could we write above each circle to show that each circle represents about ¼ of the data? 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° Answer #1 Answer #2

Explore Independent 1. Quartiles divide a data set into roughly four equally-sized parts. How could this be illustrated in the figure below? 2. What percentage could we write above each circle to show that each circle represents about ¼ of the data? 25% 25% 25% 25% 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° Q1 Q2 Q3 Q4

Explore Turn-and-talk Now that the data has been divided into four groups, form statements about the set of data below. Word Bank 25% data Between ¼ 25% 25% 25% 25% 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° Q1 Q2 Q3 Q4 “25% of the days were between 59° and 62°” “1/4 of the days were between 67° and 80°”

Explore Turn-and-talk Now that the data has been divided into four groups, form statements about the set of data below. Possible sentence starters include: “25% of the days were between…” “A quarter of the days were below…” Word Bank 25% data Between ¼ 25% 25% 25% 25% 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° Q1 Q2 Q3 Q4 “25% of the days were between 59° and 62°” “1/4 of the days were between 67° and 80°”

Explore Whole Class Could we also form statements about the data below using 50% or ½? Word Bank Greater than 50% Between data Less than ½ 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° “50% of the days were less than 64°” “Half of the days were between 62° and 67°” Hint

Explore Whole Class Could we also form statements about the data below using 50% or ½? Word Bank Greater than 50% Between data Less than ½ Possible sentence starters include: “50% of the days were between…” “Half of the days were above…” 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° “50% of the days were less than 64°” “Half of the days were between 62° and 67°” Hint

Explore Whole Class Could we also form statements about the data below using 50% or ½? Word Bank Greater than 50% Between data Less than ½ median 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° “50% of the days were less than 64°” “Half of the days were between 62° and 67°” Hint

Explore Turn and Talk Now that we know what quartiles are, what is the interquartile range?

Explore Turn and Talk Now that we know what quartiles are, what is the interquartile range? inter quartile Between Quarters

Explore Vocabulary What is the interquartile range? The interquartile range is the difference between the upper and lower quartiles in a data set. Interquartile Range = upper quartile (Q3) – lower quartile (Q1) 67° – 62° = 5° Interquartile range 59° 60° 62° 64° 65° 66° 67° 70° 80° lower quartile (Q1) upper quartile (Q3)

Practice – Part 1 Small Group Let’s go back to the test scores with a range of 98. 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 What is the interquartile range of the data?

Practice – Part 1 Whole Class 1) Find the median 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 Median = 83 points

Practice – Part 1 Whole Class Find the median Find the lower quartile (Q1): the median of all values below the median Lower quartile (Q1) = 74 points 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105

Practice – Part 1 Whole Class Find the median Find the lower quartile (Q1): the median of all values below the median Find the upper quartile (Q3): the median of all values above the median 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 Upper quartile (Q3) = 89 points

Practice – Part 1 Whole Class Interquartile Range = 89 – 74 = 15 points Lower quartile (Q1) = 74 points 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105 Upper quartile (Q3) = 89 points

Practice – Part 1 Think-Pair-Share Interquartile Range = 89 – 74 = 15 points What does an interquartile range of 15 points actually mean? 7 68 70 72 76 80 82 84 85 87 88 90 92 93 105