Understanding Box Plots, Interquartile Range, and Outliers, Exercises of Mathematical Statistics

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Notes Unit 8: Interquartile

Range, Box Plots, and Outliers

I. Box Plot

A. What is it?

• Also called a ‘Box and Whiskers’ plot
  • A 5-numbered summary of data:
    • Lower extreme
    • Lower quartile
    • Median
    • Upper quartile
    • Upper extreme
• To draw a Box Plot, we need to find all 5 of these numbers

C. Examples

Example 1:

Step 1: Order the numbers from smallest to largest

2. Find the median. The median is the middle number. If the data has two middle numbers, find the mean of the two numbers. What is the median?

Step 2 – Find the Median

Median: 12

3. Find the lower and upper medians or quartiles. These are the middle numbers on each side of the median. What are they?

Step 2 – Upper & Lower Quartiles

Median: lower^12 quartile:

upper quartile: 14

Now you are ready to construct the actual box & whisker plot. First you will need to draw an ordinary number line that extends far enough in both directions to include all the numbers in your data:

Step 3 – Draw the Box Plot

Locate the lower median 8.5 and the upper median 14 with similar vertical lines:

• Next, draw a box using the lower and upper median lines as endpoints:

3 1 2 4 5 Name the parts of a Box-and-Whisker Plot Median Upper Quartile Lower Quartile Lower Extreme Upper Extreme

II. Interquartile Range

The interquartile range is the

difference between the upper

quartile and the lower

quartile.

B. Finding Outliers

• Data: 10, 23, 6, 8, 9, 8 Outlier _____
• Data: 78, 80, 82, 79, 105, 77 Outlier _____

Ex 1: Ms. Gray is 25 years old. She took a class with students who were 55, 52, 59, 61, 63, and 58 years old. Find the mean and median with and without Ms. Gray’s age. mean ≈ 53.3 median = 58 mean = 58 median = 58. Data with Ms. Gray’s age : Data without Ms. Gray’s age : C. The Effect of Outliers