Lower Quartile (median of the lower half of the data set)

Upper Quartile (median of the upper half of the data set)

Upper Extreme or Maximum Value

Lower Extreme or Minimum Value

Pre-Algebra

Essential Questions: How do we create box and whisker plots? What do these graphs tell us about a data set?

Lesson Summary

Box and Whisker Plots

A box and whisker plot (also known as a box plot) is a graph that represents data from a five-number summary. These numbers are the median, lower and upper quartile, lower extreme and upper extreme. Consider the data set below that displays the test scores of 9 students.

50, 60, 65, 65, 70, 75, 80, 85, 90, 90, 95

50 60 65 65 70 75 80 85 90 90 95

Test Grades

Before reviewing the lesson and completing the practice problem set, watch the VIDEO!

Median (divides the data into to equal groups)

Median: 55 UQ: 58 LQ: 53

Highest – Lowest: 63 – 50 = 13

UQ – LQ: 58 – 53 = 5

Heights (inches)

Examples 1. The data below represents the heights of 12 students in inches.

52, 54, 58, 54, 56, 50, 58, 53, 59, 63, 53, 56

50 52 53 53 54 54 56 56 58 58 59 63

a) Create a box and whisker plot for the data set.

b) Calculate the range of the data.

c) Calculate the interquartile range (IQR) of the data.

2. The accompanying diagram shows a box plot of student test scores on a spelling test.

a) What is the median of the data set? 80

b) What is the lowest score a student received? 65

c) What is the highest score a student received? 100

d) What is the range of the data? 100 – 65 = 35

e) What is the upper quartile? 90

f) What is the lower quartile? 70

g) What is the interquartile range of the set of data (IQR)? 90 – 70 = 20

h) About what percentage of students scored between a 70 and 90? 50%

Lower Extreme: 50

Lower Quartile: 53

Median: 55

Upper Quartile: 58

Upper Extreme: 63

The interquartile range (IQR) is the range of values in a statistical distribution that lies between the upper and lower quartiles. To find the IQR (the range between the upper and lower quartiles), subtract the lower quartile from the upper quartile (UQ – LQ)

A box and whisker plot divides the data into 4 equal groups so ¼ or 25% of the data lies in between each section. The reason why the four sections aren’t equal in size because the range of each set of data in that section is different. The box shows the range of 50% of the data set.

The range is the difference between the upper and lower extremes.

Practice Problem Set ATTENTION ALL PRE-ALGEBRA STUENTS: We want to remind you that you and your peers create a learning

community. We encourage you to face time, text or use any other appropriate communication to reach out to a

friend and discuss your answers to the following questions. Working together and having meaningful mathematical

discussions aids in your understanding of the subject matter.

1. Jason saves a portion of his salary from his part-time job in the hope of buying a used car. He recorded

the number of dollars he was able to save over the past 15 weeks. Create a box and whisker plot for the set of data.

Dollars saved: 19, 12, 9, 7, 17, 10, 6, 18, 9, 14, 19, 8, 5, 17, 9

Minimum Value:_________ Maximum Value: _________ Median: _________ Lower Quartile: _________ Upper Quartile: _________

2. Examine the box plot pictured to the right and complete a – d.

a) What is the value of the upper quartile?

b) What is the median score?

c) What is the interquartile range of the data set?

d) What is the range of the data set? 3. A movie theater recorded the number of tickets sold daily for a popular vampire movie during the

month of December. The box plot shows the data for the number of tickets sold, in hundreds. Determine whether the following statements are true or false.

a) 25% of the data is between 300 and 400

b) The lower quartile is 300

c) 50% of the data is between 300 and 600

d) The interquartile range is 800

Make sure you check your answers with the ANSWER KEY!

Dollars Saved