Question

measures of center

the graph shows the ages of different concertgoers who have backstage passes.

which statement is true about the graph?

• a late arrival who is 21 years old with a backstage pass will make the mean greater than the median.
• the ages of concertgoers with backstage passes are skewed left, so the mean age is less than the median age.
• the two holders of backstage passes whose ages are above 40 make the mean age higher than the median age.
• a concertgoer who is 18 years old and wins a backstage pass will pull the mean more than 2 years less than the median.

Explanation:

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<reasoning>

Analyze the shape of the distribution

Using the Measures of Center knowledge point

• The histogram shows a peak in the age range of 18–21 years.
• The distribution has a long tail extending to the right, up to 48 years.
• This right-skewed shape indicates that most concertgoers are young, with a few much older individuals.

Compare the mean and median

Using the Measures of Center knowledge point

• For a right-skewed distribution, the mean is pulled toward the long tail.
• Thus, the mean age is greater than the median age.
• The two older concertgoers above age 40 act as high-value data points that pull the mean upward.

Evaluate the given statements

Using the Measures of Center knowledge point

• Statement 1: A 21-year-old is near the center/peak, so adding this value will not make the mean significantly greater than the median.
• Statement 2: The distribution is skewed right, not skewed left.
• Statement 3: The two holders above 40 are outliers that pull the mean to be higher than the median. This is correct.
• Statement 4: An 18-year-old is near the peak and will not pull the mean significantly.

</reasoning>

<answer>
<mcq-option>A late arrival who is 21 years old with a backstage pass will make the mean greater than the median.</mcq-option>
<mcq-option>The ages of concertgoers with backstage passes are skewed left, so the mean age is less than the median age.</mcq-option>
<mcq-correct>The two holders of backstage passes whose ages are above 40 make the mean age higher than the median age.</mcq-correct>
<mcq-option>A concertgoer who is 18 years old and wins a backstage pass will pull the mean more than 2 years less than the median.</mcq-option>
</answer>

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Answer:

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<reasoning>

Analyze the shape of the distribution

Using the Measures of Center knowledge point

• The histogram shows a peak in the age range of 18–21 years.
• The distribution has a long tail extending to the right, up to 48 years.
• This right-skewed shape indicates that most concertgoers are young, with a few much older individuals.

Compare the mean and median

Using the Measures of Center knowledge point

• For a right-skewed distribution, the mean is pulled toward the long tail.
• Thus, the mean age is greater than the median age.
• The two older concertgoers above age 40 act as high-value data points that pull the mean upward.

Evaluate the given statements

Using the Measures of Center knowledge point

• Statement 1: A 21-year-old is near the center/peak, so adding this value will not make the mean significantly greater than the median.
• Statement 2: The distribution is skewed right, not skewed left.
• Statement 3: The two holders above 40 are outliers that pull the mean to be higher than the median. This is correct.
• Statement 4: An 18-year-old is near the peak and will not pull the mean significantly.

</reasoning>

<answer>
<mcq-option>A late arrival who is 21 years old with a backstage pass will make the mean greater than the median.</mcq-option>
<mcq-option>The ages of concertgoers with backstage passes are skewed left, so the mean age is less than the median age.</mcq-option>
<mcq-correct>The two holders of backstage passes whose ages are above 40 make the mean age higher than the median age.</mcq-correct>
<mcq-option>A concertgoer who is 18 years old and wins a backstage pass will pull the mean more than 2 years less than the median.</mcq-option>
</answer>

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