Interpreting Box and Whisker Plots
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- Alison Stevens
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1 Algebra 1 Unit 1 Interpreting Box Plots Name: _ Date: Period: Interpreting Box and Whisker Plots A box and whisker plot easily shows us the data s (distribution). In addition to the measures of central tendency, the (measures of spread) help us to describe the data. The measures of spread the we will discuss are: o Range o Quartiles (Q 1 and Q 3) o IQR o Standard Deviation To properly describe the distribution of a data set, we use both! In particular, we use them to draw our box plots. Label the parts of the box and whisker plot below. 1. The box and whisker plot shows the daily snowfall in mm for 12 days last January. a. Label the four 25% sections of the distribution of the data set. b. What is the range? c. What is the IQR? d. What percent of the daily snowfall recorded was between 14 mm and 18 mm? What fraction is this? e. What percent of the daily snowfall recorded was less than 14 mm? What fraction is this? f. What percent of the daily snowfall recorded was greater than 14 mm? What fraction is this?
2 2. Nested Box Plots Fuel Economy: The following box and whisker plots show the average miles per gallon of gasoline used in city driving for models of small cars and SUV s (sport utility vehicles). a. Compare the number of small cars that get less than 25 miles per gallon with those that get more than 25 miles per gallon. Use percentages and actual numbers in your comparison. b. What percent of the SUV s get less than 14 miles per gallon? What is this fraction? c. What is the median miles per gallon for small cars? For SUV s? d. What is the IQR of the distribution of the fuel economy for small cars? For SUV s? e. What is the range of the distribution of the fuel economy for small cars? For SUV s? f. What is the shape of the distribution of fuel economy for small cars? How do you know this? g. What is the shape of the distribution of fuel economy for SUV s? How do you know this? h. Make a conclusion comparing the fuel economy of the two different types of vehicles.
3 3. Refer to the following box and whisker plot that shows the test results of a math class. Test Scores (as %) for 6 th Period a. What was the high score on the test? b. What percent of the class scored above a 72? c. What was the median score on the test? d. What percent of the class scored between 88 & 96? e. Do you think that this test was too hard for the students? Explain. f. Would you expect the mean to be above or below the median? Explain.
4 4. Refer to the following box and whisker plot that shows how much time was spent per night on homework for a freshman class during September. Average Minutes per Night Spent on Homework a. What percent of the freshmen spend more than 60 minutes on homework per night? b. What is the range of times that the middle 50% of the freshmen spend on homework per night? c. What percent of the freshmen spend less than 20 minutes per night on homework? d. Would you expect the mean number of minutes per night to be higher or lower than the median? Explain.
5 5. Refer to the box and whisker plots below that compare homework time per night with TV time per night for the same group of freshmen. TV & Homework Minutes per Night Homework Time TV Time a. What percent of the freshmen watch TV for at least 15 minutes per night? b. What is the 3 rd quartile for the TV time data? c. Is it more common for a freshman at this high school to spend more than 1 hour on homework or more than 1 hour watching TV? Explain. For questions 6-14, identify if each statement is true, false, or cannot be determined. 6. Some freshmen didn t watch TV that month. 7. The TV box & whisker graph contains more data than the homework graph % of the freshmen spend between 48 & 60 minutes per night on homework % of the freshmen didn t watch TV that month. 10. In general, these freshmen spend more time watching TV than doing homework. 11. The TV data is more varied than the homework data. 12. The ratio of freshmen who spend more than 110 minutes per night watching TV to those who spend less is about 2: freshmen watch TV. 14. Twice as many freshmen watch TV for more than 1 hour than do homework for more than 1 hour.
6 15. Suppose that one family kept track of how many Redbox DVDs they rented each month for a two year period. The numbers for each month are shown in the table below. Make a box & whisker graph from this data. J F M A M J J A S O N D J F M A M J J A S O N D
7 16. Refer to the following box and whisker plots below that show the average monthly high temperatures for Milwaukee, Wisconsin & Honolulu, Hawaii. Average Monthly High Temperatures Milwaukee Honolulu a. Write a short paragraph comparing the temperatures in both cities. Use complete sentences. _
8 HOMEWORK: In the table below, the average monthly temperatures for Pullman and Seattle are shown. Draw a box and whisker plot (using the same scale) for each city from the data. Then write a short paragraph summarizing what your graphs tell you. Summary: Month Pullman Averages Seattle Averages January February March April May June July August September October November December
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