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Comparing Distributions in Context

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Comparing Distributions in Context

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Part 1: Comparing commute-time distributions

Context: A school is investigating how long students spend travelling to school. The times below are in minutes. Each group contains 12 students.

School A: 12, 15, 18, 20, 21, 22, 24, 25, 27, 29, 31, 34

School B: 8, 12, 16, 18, 20, 23, 29, 35, 41, 44, 46, 52

1. Find the median commute time and range for each school. Show your working.
2. What proportion of students have a commute of 20 minutes or less at each school? Give each answer as a fraction and a percentage.
3. Which school has the greater spread of commute times? Use a statistic from the data as evidence.
4. A student wants a commute that is usually short and reasonably predictable. Which school would you recommend? Complete the sentence and justify your choice.

I recommend School ______ because the typical commute is ______ minutes, the range is ______ minutes, and ______________________________.

Part 2: Trends, unusual values and limitations

Context: A school recorded the percentage of students bringing a reusable drink bottle over five months.

School A: January 32%, February 35%, March 34%, April 38%, May 41%

School B: January 40%, February 39%, March 41%, April 40%, May 39%

5. Describe the overall trend for each school. Use data values in your answer.
6. In May, how many percentage points higher was School B than School A? What does this comparison show?
7. School A claims, “Our reusable-bottle rate is improving.” Is this claim supported by the data? Explain, including any variation or unusual value.
8. State one limitation of using only these five monthly percentages to predict what will happen next term.

One limitation is that ________________________________________________.

9. Write a justified conclusion for a school leader whose purpose is to identify which school needs a campaign to increase reusable-bottle use.

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