Question

the graph shows the ages of different concertgoers who have backstage passes.
backstage passes
which statement is true about the graph?
○ a late arrival who is 21 years old with a back-stage pass will make the mean greater than the median.
○ the two holders of back-stage passes whose ages are above 40 make the mean age higher than the median age.
○ the ages of concert-goers with backstage passes are skewed left, so the mean age is less than the median age.
○ a concert-goer who is 18 years old and wins a back-stage pass will pull the mean more than 2 years less than the median.

Explanation:

Step1: Calculate total concertgoers

Add frequencies: $3+6+8+6+5+3+2=33$

Step2: Find median position

Median is $\frac{33+1}{2}=17$th value, in 21-24 age group.

Step3: Analyze skew and mean/median

Graph is right-skewed (tail right). For right skew, mean > median.

Step4: Evaluate each option

• 21yo is in median group: won't make mean > median.
• Two 40+ are outliers: pull mean up, so mean > median.
• Skew is right, not left: mean > median.
• 18yo is close to median: won't pull mean 2+ below median.

Answer:

The two holders of back-stage passes whose ages are above 40 make the mean age higher than the median age.