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Comparing Distributions in Context

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Comparing Distributions in Context

Use the data displays to support your answers. Show calculations where appropriate. Give percentages to one decimal place when needed.

Commute-time distributions

Two schools recorded the one-way commute times, in minutes, of 12 students at each school.

School K: 11, 14, 17, 19, 21, 23, 24, 26, 28, 30, 33, 36

School M: 7, 10, 15, 18, 22, 25, 31, 37, 40, 43, 49, 55

1.For School K, the 12 commute times are 11, 14, 17, 19, 21, 23, 24, 26, 28, 30, 33 and 36 minutes. For School M, they are 7, 10, 15, 18, 22, 25, 31, 37, 40, 43, 49 and 55 minutes. Find the median and range for each school. Show your working.

2.Among the 12 students at each school, what proportion had a commute of 22 minutes or less? Give the proportion for each school as a simplified fraction and a percentage.

3.School K's commute times range from 11 to 36 minutes, while School M's range from 7 to 55 minutes. Which school's commute times have the greater spread? Use a suitable statistic to support your comparison.

4.A student values a commute that is typically short and fairly consistent. School K has a median commute of 23.5 minutes and a range of 25 minutes. School M has a median of 28 minutes and a range of 48 minutes. Which school would you recommend, and why?

Trends, unusual values and limitations

A school survey recorded the percentage of students bringing a reusable drink bottle during five months.

School R — January: 31%; February: 34%; March: 33%; April: 37%; May: 40%

School T — January: 39%; February: 40%; March: 38%; April: 39%; May: 38%

5.School R recorded 31%, 34%, 33%, 37% and 40% from January to May. School T recorded 39%, 40%, 38%, 39% and 38% over the same months. Describe the overall trend for each school, using values from the data.

6.In May, 38% of surveyed students at School T and 40% at School R brought a reusable bottle. How many percentage points higher was School R's result, and what does this comparison tell you?

7.School R says its reusable-bottle rate is improving. Its monthly results were 31%, 34%, 33%, 37% and 40% from January to May. Is the claim supported? Explain using the overall pattern and any variation in the data.

8.Only five monthly percentages are available for School R: 31%, 34%, 33%, 37% and 40%. State one limitation of using these data to predict the reusable-bottle rate next term.

9.A school leader wants to decide which school most needs a campaign to increase reusable-bottle use. School R recorded 31%, 34%, 33%, 37% and 40% from January to May; School T recorded 39%, 40%, 38%, 39% and 38%. Write a justified conclusion using the levels and trends in both sets of data.

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Comparing Distributions in Context

Comparing Distributions in Context

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2 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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