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Understanding Box-and-Whisker Plots for Data Analysis

Learn how to create a box-and-whisker plot step by step, including finding quartiles, outliers, and drawing the plot accurately.

markhardy
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Understanding Box-and-Whisker Plots for Data Analysis

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  1. Third Quartile

  2. Median

  3. First Quartile

  4. Upper Extreme

  5. Interquartile Range

  6. Lower Extreme

  7. Outlier

  8. Box and Whisker Plot

  9. Step 1 – Order Numbers Order the set of numbers from least to greatest.

  10. Step 2 – Find the Median 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?

  11. Step 3 – First & Third Quartiles Find the lower, or first quartile and upper, or third quartiles. These are considered the lower and upper medians. These are the middle numbers on each side of the median. What are they in this example?

  12. Interquartile Range The interquartile range is the difference between the upper quartile and the lower quartile. 14 – 8.5 = 5.5

  13. Step 4 – Draw a Number Line Now you are ready to construct the actual box & whisker graph. 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:

  14. Step 5 – Draw the Parts Locate the median using a vertical line just above your number line:

  15. Step 5 – Draw the Parts Locate the first quartile and the third quartile with similar vertical lines:

  16. Step 5 – Draw the Parts Next, draw a box using the lower and upper median lines as endpoints:

  17. Step 5 – Draw the Parts Finally, the whiskers extend out to the data's smallest number, 5 and largest number, 20: Outliers are not included in the box and whisker plot. They are shown as an asterisks on the number line. For example, if the data set had an outlier of 24, it would be show as seen below.

  18. Step 6 - Label the Parts of a Box-and-Whisker Plot First Quartile Median Third Quartile 3 1 2 Upper extreme2 Lower extreme 4 5 Outliers are not included in the box and whisker plot. They are shown as an asterisks on the number line.

  19. Drawing a Box Plot. Example 1: Draw a Box plot for the data below 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Q2 Q1 Q3 Upper Quartile = 9 Lower Quartile = 5½ Median = 8 4 5 6 7 8 9 10 11 12

  20. Drawing a Box Plot. Example 2: Draw a Box plot for the data below 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Q2 Q3 Q1 Upper Quartile = 10 Lower Quartile = 4 Median = 8 12 13 3 4 5 6 7 8 9 10 11 14 15

  21. Drawing a Box Plot. Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data. Q2 Qu QL 115, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186 Upper Quartile = 180 Lower Quartile = 158 Median = 171 130 140 150 160 170 180 cm 190

  22. Practice Use the following set of data to create a box plot. 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

  23. Median What is the median or 2nd quartile? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The median is 39

  24. 1st Quartile What is the 1st quartile? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The lower quartile is 11

  25. 3rd Quartile What is the 3rd quartile? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The third quartile is 61

  26. What is the Interquartile Range? 50

  27. Outliers An outlier is a number that falls outside the limits. Are there any outliers? The outlier is 220

  28. c Upper Extreme What is the upper extreme? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The upper extreme is 99

  29. Lower Extreme What is the lower extreme limit? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The lower extreme is 3

  30. Graphing The Data Now use the data you have collected to create a box and whisker plot.

  31. Worksheet 1 Independent Practice – Create box plots for the following data Example 1: Draw a box plot for the data below. 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10 Example 2: Draw a box plot for the data below. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10

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