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Comparing Numerical Data Using Box Plots

Comparing Numerical Data Using Box Plots. Warm Up. OBJECTIVE: SWBAT compare numerical data using box plots. Language Objective: SWBAT verbally analyze and compare data using content specific vocabulary. If your job is to recommend a ski resort by comparing the annual

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Comparing Numerical Data Using Box Plots

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  1. Comparing Numerical Data Using Box Plots

  2. Warm Up OBJECTIVE: SWBAT compare numerical data using box plots. Language Objective: SWBAT verbally analyze and compare data using content specific vocabulary. If your job is to recommend a ski resort by comparing the annual snowfall of two mountains for the past 50 years, how would you compare all the data? (Hint: What are some measures we have been using to compare sets of data?) 1962 1963 1964 1965 1966 1967 … Powder Valley Mad Mountain 217 in. 132 in. 310 in. 104 in. 186 in. 287 in. … 107 in. 233 in. 207 in. 106 in. 229 in. 37 in. … Mean, Median, Minimum, Maximum, Q1, Q3 Agenda

  3. Launch 1962 1963 1964 1965 1966 1967 … Powder Valley Mad Mountain 217 in. 132 in. 310 in. 104 in. 186 in. 287 in. … 107 in. 233 in. 207 in. 106 in. 229 in. 37 in. … What are some of the ways we can represent this data visually so we can compare it more easily? Agenda

  4. Launch Think-Pair-Share 1962 1963 1964 1965 1966 1967 … Powder Valley Mad Mountain 217 in. 132 in. 310 in. 104 in. 186 in. 287 in. … 107 in. 233 in. 207 in. 106 in. 229 in. 37 in. … We have been using box plots to summarize sets of data. How could we show 2 sets of data on a box plot? Sketch what that might look like. (box plots on next slide)

  5. Launch Whole Class Powder Valley Mad Mountain 0 50 100 150 200 250 300 350 400 Annual Snowfall (inches) Agenda

  6. Launch How can we use this box plot to compare the two ski resorts? (Hint: Is there a way to use the box plot to compare the values from the five number summary for each resort?) Powder Valley Mad Mountain 0 50 100 150 200 250 300 350 400 Annual Snowfall (inches) Agenda

  7. Explore Whole Class From the box plot, you can easily see the median snowfall for each resort. Powder Mad Valley Mountain Median 175 inches 225 inches Powder Valley Mad Mountain 0 50 100 150 200 250 300 350 400 Annual Snowfall (inches) Agenda

  8. Explore Whole Class Using the medians to compare the resorts, which resort appears to be better? Powder Mad Valley Mountain Median 175 inches 225 inches Powder Valley Mad Mountain 0 100 250 50 150 200 300 350 400 Annual Snowfall (inches) Agenda

  9. Explore Whole Class Using the box plot, you can identify the record high (maximum) and record low (minimum) annual snowfalls for each resort. Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Powder Valley Mad Mountain 0 100 250 50 150 200 300 350 400 Annual Snowfall (inches) Agenda

  10. Explore Whole Class Using the minimum values to compare the resorts, which resort appears to be better? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Powder Valley Mad Mountain 0 100 250 50 150 200 300 350 400 Annual Snowfall (inches) Agenda

  11. Explore Whole Class Using the maximum values to compare the resorts, which resort appears to be better? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Powder Valley Mad Mountain 0 100 250 50 150 200 300 350 400 Annual Snowfall (inches) Agenda

  12. Explore Think-Pair-Share What does the distance between points in the box plot tell you about how spread out the data is? The greater the distance between points in the box plot, the more spread out the annual snowfall data is. Powder Valley Mad Mountain 0 50 100 150 200 250 300 350 400 Agenda Hint

  13. Explore Think-Pair-Share What does the distance between points in the box plot tell you about how spread out the data is? The greater the distance between points in the box plot, the more spread out the annual snowfall data is. Powder Valley Mad Mountain 0 50 100 150 200 250 300 350 400 Agenda Hint

  14. Explore Whole Class Which mountain varies less in terms of the amount of snowfall from year to year? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Variationsmall large Powder Valley Mad Mountain 0 100 250 50 150 200 300 350 400 Annual Snowfall (inches) Agenda

  15. Explore Whole Class Which resort has a greater chance of receiving more than 300 inches of snow? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Variationsmall large Chance of >300 in. lesser greater Powder Valley Mad Mountain 0 250 50 100 150 200 300 350 400 Annual Snowfall (inches) Agenda

  16. Explore Small Group Which resort would you recommend? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Variationsmall large Chance of >300 in. lesser greater Agenda

  17. Explore Think-Pair-Share How does the data gathered below relate to the pieces of a five number summary? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Variationsmall large Chance of >300 in. lesser greater Powder Valley Mad Mountain 0 250 50 100 150 200 300 350 400 Annual Snowfall (inches) Agenda

  18. Explore Whole Class Original Question: If your job is to recommend a ski resort by comparing the annual snowfall between two mountains for the past 50 years, how would you compare all the data? How did we use the box plot to answer this question? Powder Valley Mad Mountain 0 100 250 50 150 200 300 350 400 Annual Snowfall (inches) Agenda

  19. Practice – Sharing Question #1 A farmer starts 9 tomato plants in a greenhouse several weeks before spring. The seedlings look a little small this year so the farmer decides to compare this year’s growth with last year’s growth. This year’s growth is measured in inches as: 12 8.4 10 9.8 14 7.9 11 12.7 13.7 Last year’s growth was measured in inches as: 11.7 9 17 10.5 13.4 15.2 16.8 11.5 15 Should the farmer be concerned about the tomato plants this year? Why or why not? Support your answer by creating a box plot. Agenda

  20. Practice – Sharing Question #1 This year’s growth is measured in inches as: 12 8.4 10 9.8 14 7.9 11 12.7 13.7 7.9 8.4 9.8 10 11 12 12.7 13.7 14 9.1 13.2 Median = 11 inches Minimum = 7.9 inches Lower Quartile (Q1) = 9.1 inches Maximum = 14 inches Upper Quartile (Q3) = 13.2 inches Agenda

  21. Practice – Sharing Question #1 Last year’s growth was measured in inches as: 11.7 9 17 10.5 13.4 15.2 16.8 11.5 15 9 10.5 11.5 11.7 13.4 15 15.2 16.8 17 11 16 Median = 13.4 inches Minimum = 9 inches Lower Quartile (Q1) = 11 inches Maximum = 17 inches Upper Quartile (Q3) = 16 inches Agenda

  22. Practice – Sharing Question #1 Last Year’s Growth This Year’s Growth Agenda

  23. Practice – Sharing Question #1 This Year Last Year Minimum 7.9 9 Q1 9.1 11 Median 11 13.4 Q3 13.2 16 Maximum 14 17 Last Year’s Growth This Year’s Growth The farmer should be concerned. The box plots show that this year’s seedlings are smaller than last year’s seedlings. All of the five-number summary values are less. Agenda

  24. Practice – Sharing Question #2a Your job: Make a peanut butter recommendation for grocery shoppers. Suppose price is the only factor a buyer considers. Is natural peanut butter or regular peanut butter a better choice? Explain. Grocery shoppers should purchase regular peanut butter if price is the only factor, as all of the five-number summary values are less. Agenda

  25. Practice – Sharing Question #2b Your job: Make a peanut butter recommendation for grocery shoppers. Suppose quality is the only factor a buyer considers. Is natural peanut butter or regular peanut butter a better choice? Explain. Grocery shoppers should purchase natural peanut butter if quality is the only factor, as all of the five-number summary values are greater. Agenda

  26. Summary Think-Pair-Share 1962 1963 1964 1965 1966 1967 … Powder Valley Mad Mountain 217 in. 132 in. 310 in. 104 in. 186 in. 287 in. … 107 in. 233 in. 207 in. 106 in. 229 in. 37 in. … Methods we could have used to compare these two sets of data during our warm-up today: Mean, Median, Minimum, Maximum, Lower Quartile (Q1) and Upper Quartile (Q3) If we already have all of these strategies for comparing two sets of data, why did we learn about using box plots to compare sets of data today? Agenda

  27. The two main ideas here are: 1) Box plots allow the reader to easily see the spread of a set of data and 2) Box plots can be used to more easily compare two sets of data, as the similarities and differences are much more evident in comparison to sets of data written as lists.

  28. Assessment – Exit Ticket! Complete and hand in the Exit Ticket before you leave! Agenda

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