Question 2: Analyzing data and interpreting results

Homework minutes

Unit 1
10 points
About 22 minutes

You can use a calculator on this question, just like on exam day.

A multi-part question built on a data set or summary statistics: you calculate things like outlier fences, compare distributions, pick the right measure of center or spread, and justify a claim in context. It focuses on Practices 3 and 4. On the exam: Question 2 of 4 (official name: Multi-Focus on Practices 3 and 4). Section II has 4 free-response questions in 90 minutes (50% of the score); each question is worth 10 points and 12.5% of the score. The exam is fully digital in Bluebook, a graphing calculator with statistical capabilities is expected, and the formula sheet and tables are provided.

The question and its sources

Show the work that leads to each answer, and explain your reasoning in the context of the situation. A graphing calculator with statistical capabilities, the formula sheet and the statistical tables are available. Use the information given to answer parts A through F, and label any subparts (for example, i and ii).

The homework data

A teacher asked a random sample of 15 students in her 10th-grade classes how many minutes they spent on homework last night. The responses are in the table.

Source: Hypothetical scenario

Minutes spent on homework last night

Student	Minutes
1	45
2	30
3	60
4	20
5	140
6	50
7	35
8	40
9	65
10	25
11	45
12	70
13	30
14	55
15	40

Source: Hypothetical data

Suggested time: 22 minutes

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Part (A)

2 points

(i) Calculate the mean and standard deviation of the number of minutes. (ii) Calculate the five-number summary.

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Part (B)

1 point

Determine whether there are any outliers in the data using the 1.5 × IQR rule. Show your work.

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Part (C)

1 point

Describe the boxplot you would construct for these data. Include the axis and its label and scale, the positions of the box and the median, where each whisker ends, and how any outliers would be shown.

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Part (D)

2 points

Describe the distribution of homework time for these 15 students. (i) Describe the shape, and identify any unusual features. (ii) Describe the center and variability in context.

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Part (E)

2 points

Suppose the value of 140 minutes is removed from the data set. (i) Explain how the mean and the median would change. (ii) Explain how the standard deviation would change.

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Part (F)

2 points

Jordan, one of the students in the sample, did 70 minutes of homework. (i) Calculate the percentile of Jordan's homework time within this sample. (ii) Priya, a student in a different class, did 80 minutes of homework. In her class, homework times had a mean of 58 minutes and a standard deviation of 20 minutes. Determine which student spent more time on homework relative to their own class. Justify your answer with calculations.

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