Measures of Position Quartiles Interquartile Range Box-and-Whisker Plot Percentiles (tomorrow) z-scores (tomorrow)

Measures of Position Quartiles Fractiles – divide an ordered data set into equal parts Name one fractile you already know Q1, Q2, Q3 divide an ordered data set into 4 equal parts The median is also known as Q2

Measures of Position Quartiles Example: The test scores of 15 employees enrolled in a CPR training course are listed. Find the first, second, and third quartiles of the test scores. 13 9 18 15 14 21 7 10 11 20 5 18 37 16 17 First, order the data set and find the median (Q2) 5 7 9 10 11 13 14 15 16 17 18 18 20 21 37 Then, find the first and third quartiles (Q1 and Q3)

Measures of Position Quartiles You Try #1: Finding Quartiles The tuition costs (in thousands of dollars) for 25 universities are listed. Find the first, second, and third quartiles. 20 26 28 25 31 14 23 15 12 26 29 24 31 19 31 17 15 17 20 31 32 16 21 22 28

Measures of Position Interquartile Range The interquartile range (IQR) of a data set is the difference between the third and first quartiles IQR = Q3 – Q1 Gives an idea of how much the middle 50% of the data varies Can also be used to identify outliers The data point is an outlier if it is more than 1.5 IQRs to the left of Q1 or to the right of Q3

Measures of Position Interquartile Range Example: The test scores of 15 employees enrolled in a CPR training course are listed. Find the interquartile range. What can you conclude from the result? 13 9 18 15 14 21 7 10 11 20 5 18 37 16 17 5 7 9 10 11 13 14 15 16 17 18 18 20 21 37 IQR = Q3 – Q1 = 18-10 = 8 37 is more than 1.5 outliers from Q3, so it is an outlier.

Measures of Position Interquartile Range You Try #2: Finding the Interquartile Range The tuition costs (in thousands of dollars) for 25 universities are listed. Find the Interquartile Range and interpret the result. 20 26 28 25 31 14 23 15 12 26 29 24 31 19 31 17 15 17 20 31 32 16 21 22 28

Measures of Position Box-and-Whisker Plot A box-and-whisker plot is a tool that highlights the important features of a data set To graph a box-and-whisker plot, one must know the following values: The minimum entry The first quartile or Q1 The median or Q2 The third quartile or Q3 The maximum entry 𝑡ℎ𝑒 𝑓𝑖𝑣𝑒−𝑛𝑢𝑚𝑏𝑒𝑟 𝑠𝑢𝑚𝑚𝑎𝑟𝑦

Measures of Position Box-and-whisker plot Example: The test scores of 15 employees enrolled in a CPR training course are listed. Find the interquartile range. What can you conclude from the result? 13 9 18 15 14 21 7 10 11 20 5 18 37 16 17 Drawing a Box-and-Whisker Plot: Find the five-number summary of the data set Min = 5 Q1 = 10 Q2 = 15 Q3 = 18 Max = 37

Measures of Position Box-and-whisker plot Example: The test scores of 15 employees enrolled in a CPR training course are listed. Find the interquartile range. What can you conclude from the result? 13 9 18 15 14 21 7 10 11 20 5 18 37 16 17 Drawing a Box-and-Whisker Plot: 2. Construct a horizontal scale that spans the range of the data Min = 5 Q1 = 10 Q2 = 15 Q3 = 18 Max = 37 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Measures of Position Box-and-whisker plot Example: The test scores of 15 employees enrolled in a CPR training course are listed. Find the interquartile range. What can you conclude from the result? 13 9 18 15 14 21 7 10 11 20 5 18 37 16 17 Drawing a Box-and-Whisker Plot: 3. Plot the five numbers above the horizontal scale Min = 5 Q1 = 10 Q2 = 15 Q3 = 18 Max = 37 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Measures of Position Box-and-whisker plot Example: The test scores of 15 employees enrolled in a CPR training course are listed. Find the interquartile range. What can you conclude from the result? 13 9 18 15 14 21 7 10 11 20 5 18 37 16 17 Drawing a Box-and-Whisker Plot: 4. Draw the box Min = 5 Q1 = 10 Q2 = 15 Q3 = 18 Max = 37 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Measures of Position Box-and-whisker plot Example: The test scores of 15 employees enrolled in a CPR training course are listed. Find the interquartile range. What can you conclude from the result? 13 9 18 15 14 21 7 10 11 20 5 18 37 16 17 Drawing a Box-and-Whisker Plot: 5. Draw the whiskers Min = 5 Q1 = 10 Q2 = 15 Q3 = 18 Max = 37 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Measures of Position Box-and-Whisker Plot You Try #3: Drawing a box-and-whisker plot The tuition costs (in thousands of dollars) for 25 universities are listed. Draw a box-and-whisker plot representing the data. 20 26 28 25 31 14 23 15 12 26 29 24 31 19 31 17 15 17 20 31 32 16 21 22 28