You compare the average amounts of time people in their twenties and thirties spend driving each week. The double box-and-whisker plot represents the medians of $100$ random samples of $8$ people from each age group. Can you determine whether one age group drives more than the other? Explain.

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Solution

Step 1: Data of Twenties = $0 5 10 15 25$
Median of Twenties = $10$
IQR of Twenties = $15 - 5 = 10$
Step 2: Data of Thirties = $0 10 15 20 40$
Median of Thirties = $15$
IQR of Thirties = $20 - 10 = 10$
Step 3: Differences in medians $\div$ IQR $= 15 - 10 \div 10 = \div 10 = 0.5$
Because the quotient is less than $2$ , the difference is not significant.
Hence, because the variables are the same, you can determine that one age group drives more than the other visual overlap by expressing the differences in the medians as the multiples of IQR.

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You compare the average amounts of time people in their twenties and thirties spend driving each week. The double box-and-whisker plot represents the medians of 100 random samples of 8 people from each age group. Can you determine whether one age group drives more than the other? Explain.

You compare the average amounts of time people in their twenties and thirties spend driving each week. The double box-and-whisker plot represents the medians of $100$ random samples of $8$ people from each age group. Can you determine whether one age group drives more than the other? Explain.