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

2. 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

3. 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 First, order the data set and find the median (Q2)
Then, find the first and third quartiles (Q1 and Q3)

4. 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

5. 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

6. 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?
IQR = Q3 – Q1 = = 8
37 is more than 1.5 outliers from Q3, so it is an outlier.

7. 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

8. 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

9. 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?
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

10. 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?
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

11. 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?
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

12. 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?
Drawing a Box-and-Whisker Plot: 4. Draw the box
Min = 5
Q1 = 10
Q2 = 15
Q3 = 18
Max = 37

13. 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?
Drawing a Box-and-Whisker Plot: 5. Draw the whiskers
Min = 5
Q1 = 10
Q2 = 15
Q3 = 18
Max = 37

14. 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