Warm Up Problem Simplify the expression: 9 + 43 x (20 – 8) ÷2 + 6

Measures of Variation Lesson 11-3 Part 1

Objectives I can find the measures of variation. I can define outlier, range, interquartile range, and quartile.

Vocabulary measures of variation – used to describe the distribution (spread) of data quartile – values that divide the data set into 4 equal parts 1st and 3rd quartiles – the medians of the data values less than the median and greater the median, respectively

Vocabulary Continued interquartile range (IQR) – the distance between the 1st and 3rd quartiles of the data set range – the difference between the greatest and least data values

Notes Measures of variation of a data set are shown below.

Example 1 Find the measures of variation for the data. Range = Max – Min = 70 – 1 = 69 mph Quartiles: Order the numbers. Q1 median Q3 (27.5) 1 8 25 30 50 70 IQR = Q3 = Q1 50 – 8 = 42

Got It? 1. Determine the measures of variation for the data 64, 61, 67, 59, 60, 58, 57, 71, 56, and 62.

Homework C = #1a – c, 2, 3, 4 A = #7

Measures of Variation Lesson 11-3 Part 2

Note: An outlier must be beyond 1.5 times the IQR Vocabulary outlier – a data point that is much larger or much smaller than the median Note: An outlier must be beyond 1.5 times the IQR

Example 2 The ages of candidates in an election are 23, 48, 49, 55, 57, 63, and 72. Name any outliers in the data. Find the IQR: Q3 – Q1 23, 48, 55, 57, 63, 72 63 – 48 = 15 Q3 median Q1

Example 2 The ages of candidates in an election are 23, 48, 49, 55, 57, 63, and 72. Name any outliers in the data. Multiply the IQR by 1.5: 15 x 1.5 = 22.5 Take the Q1 and subtract 22.5: 48 – 22.5 = 25.5 Take the Q3 and add 22.5: 63 + 22.5 = 85.5

Example 2 The ages of candidates in an election are 23, 48, 49, 55, 57, 63, and 72. Name any outliers in the data. Are there any numbers less than 25.5 and/or greater than 85.5? Yes, so the only outlier is 23.

Got It? 2. The lengths, in feet, of various bridges are 88, 251, 275, 354, and 1,121. Name any outliers in the data set.

Example 3 The table shows a set of scores on a science test in two different classrooms. Compare and contrast their measures of variation.

Example 3 Both classrooms have a range of 35 points. Room A has a lower median than Room B. Room B has a higher IQR than Room A.

Got It? 3. Temperatures for the first half of the year are given for Antelope, Montana and Augusta, Maine. Compare and contrast the measures of variation for the two cities. Answer these questions: Who has the largest range? Who has the largest median? Who has the largest IQR?

C = #1d, 5, 8, 11 A = #6, 10 Homework Hint: #8. Q1 Q3

Homework Hints When it says “compare and contrast their measures of variations”, answer these questions: Who has the higher range? Who has the higher median? Who has the higher IQR?