Lesson 16

Compare & Contrast

  • Let’s analyze data

16.1: Math Talk: Measuring Up

What is the distance between the markings?

Image of ruler. Arrow at 3 inches and 11 inches.
Image of ruler. Arrow at 2 point 5 inches and 11 inches.
Image of ruler. Arrow at 2 point 25 inches and 11 inches.
Image of ruler. Arrow at 1 and one eighth inches and 11 inches.

 

16.2: Compare & Contrast

Here are the shoe sizes from two cohorts in the military.

Cohort A:

Box plot from 6 to 12 by 1's. Whisker from 6 to 6 point 5. Box from 6 point 5 to 8 point 5 with vertical line at 7 point 5. Whisker from 8 point 5 to 9.  

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Cohort B:

Box plot from 6 to 12 by 1's. Whisker from 8 to 8 point 25. Box from 8 point 25 to 11 with vertical line at 9 point 5. Whisker from 11 to 12.  
  1. Is there any overlap between the two data sets? Explain your reasoning.
  2. Which cohort has more variability?
  3. Does at least one person from cohort A have a bigger shoe size than someone from cohort B? Explain your reasoning.
  4. Compare the measures of center.

16.3: Compare & Contrast Continued

Many shoes on the floor

Here are the shoes sizes of some grade 9 and grade 12 students.

Grade 9 shoe sizes:

  • 6
  • 8
  • 6.5
  • 7.5
  • 7
  • 6.5
  • 9
  • 6
  • 8.5
  • 7.5
  • 8
  • 10
  • 11
  • 8
  • 9

Grade 12 shoe sizes:

  • 10
  • 9
  • 10.5
  • 8.5
  • 10
  • 9
  • 9.5
  • 8
  • 8
  • 11
  • 9
  • 9.5
  • 11
  • 10.5
  • 8.5
  1. Create a box plot, dot plot, or histogram to represent both sets of data.
  2. Describe the distribution shapes.
  3. Complete the table.
      mean median IQR standard deviation
    grade 9
    shoe sizes    		        
    grade 12
    shoe sizes    		        
  4. Does one grade’s shoe sizes have more variation than the other? Explain how you know.
  5. Compare the measures of center for the two sets of shoe sizes.
  6. Do the distributions overlap? Use the data display you created to explain how you know.

Summary