Pre-Algebra

Essential Questions: How do we compare box plots? What conclusions can we make from analyzing box plots?

Lesson Summary Comparing Box Plots (aka: Box and Whisker Plots)

Consider the box plots below that display two class sets of test scores.

Min Q1 Q2 Q3 Max Range IQR

Class A 20 60 70 85 95 75 25

Class B 50 61 80 98 100 50 37

Making Inferences/Drawing Conclusions:

Recall that a box and whisker plot only displays a summation of the data using 5 measures (lowest value, highest value, lower quartile, upper quartile and median). We can examine variability (the spread of the data set) using the range or interquartile range.

From the box plots above, we cannot see test scores of class A and class B but we can draw some conclusions about how the classes performed overall.

Even though the range of scores in Class A is greater than the range of scores in Class B, the students in Class A performed more consistently. The IQR shows that 50% of the students in class A scored within a range of 25 points. In class B, 50% of the students scored within a range of 37 points.

It is reasonable to assume that the low test score of 20 is most likely an outlier creating a large range in Class A. Even though Class A’s scores are more consistent, Class B outperformed Class A. The median score in class B is greater than the median score in class A. Half the class scored at least an 80 or above as compared to Class A in which half the class scored at least a 70 or above.

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

Class A Range: 95 – 20 = 75 IQR: 85 – 60 = 25

Class B Range: 100 – 50 = 50 IQR: 98 – 61 = 37

Examples 1. The box-and-whisker plots below represent the number of points scored in each game of the 2001- 2002 season for the New England Patriots and the St. Louis Rams.

What conclusions can you make about the data sets? How do the teams compare? Justify your response. During the 2001-2002 season, the Rams were the more consistent team. Both the range and interquartile range is less than the range and interquartile range of the Patriots. The Rams show less variability (less spread) in scoring points. When comparing the medians of both data sets, we can also conclude that the Rams outperformed the Patriots during the season. In half the games, the Rams scored more than 32.5 points. In only 25% of their games, the Patriots scored more than 31.5 points. Multiple Choice 2. The accompanying box-and-whisker plots can be used to compare the annual incomes of three professions. Based on the box-and-whisker plots, which statement is true?

A. The median income for nuclear engineers is less than the median income for musicians.

B. All nuclear engineers earn more than all police.

C. The median income for police officers and musicians is the same.

D. The range of annual incomes of police officers is greater than the range of annual incomes of musicians.

Range: 44 – 3 = 41 IQR: 31.5 – 17 = 14.5

Range: 48 – 15 = 33 IQR: 36.5 – 25.5 = 11

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.

Multiple Choice

1. Corinne is planning a beach vacation in July and is analyzing the daily high temperatures for her potential destinations. She wants to choose a destination with a high median temperature and a small interquartile range. She constructed box plots shown in the diagram below. Which destination has a median temperature above 80 degrees and the smallest interquartile range? A. Ocean Beach B. Whispering Palms C. Serene Shores D. Pelican Beach 2. What conclusion can be drawn from the box-and-whisker plots below?

A. Men generally weigh more than women.

B. Women generally weigh more than men.

C. Men and women generally weigh the same.

D. There is no conclusion that can be drawn from this data.

3. Consider the box plots below that show the distribution of the number of team wristbands sold daily by two different stores over the same time period. Which statement regarding the two plots is false?

A. Store A has a greater spread than store B.

B. Store B has a greater number of sales overall.

C. Store A’s median is very close to store B’s minimum.

D. Store A and store B have the same interquartile range.

Extended Response 4. The box plots below show the ages of film viewers for three different movies. Analyze the graphs and answer the questions that follow. Justify your responses. Use evidence from the graphs to support your reasoning and explanations.

a) Which film do you think would appeal to the whole family? Explain your response.

b) Which film do you think would appeal to teenagers? Explain your response.