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Members of the Valley View Soccer League sold raffle tickets to help pay for new goalposts and nets. On one team, all $18$ players sold at least $5$ tickets, and some sold more than $25$ tickets. The median number of tickets sold by this team was $12.5$ tickets, and the interquartile range was $15$ tickets. $\newline$ Which is a measure of how much the number of tickets sold by this team varied? $\newline$ Choices: $\newline$ (A) $5$ tickets $\newline$ (B) $12.5$ tickets $\newline$ (C) $15$ tickets $\newline$ (D) $25$ tickets $\newline$

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Interpret confidence intervals for population means

Full solution

Q. Members of the Valley View Soccer League sold raffle tickets to help pay for new goalposts and nets. On one team, all

18

players sold at least

5

tickets, and some sold more than

25

tickets. The median number of tickets sold by this team was

12.5

tickets, and the interquartile range was

15

tickets.

\newline

Which is a measure of how much the number of tickets sold by this team varied?

\newline

Choices:

\newline

(A)

5

tickets

\newline

(B)

12.5

tickets

\newline

(C)

15

tickets

\newline

(D)

25

tickets

\newline

Understand question: Step $1$ : Understand the question and identify the key information. $\newline$ The question asks for a measure of how much the number of tickets sold varied among the team players. The choices given are different statistical measures.
Identify measure: Step $2$ : Identify the correct statistical measure for variability. $\newline$ The interquartile range (IQR) is a measure of statistical dispersion, or how spread out the numbers are in a set. It is calculated as the difference between the $75^{\text{th}}$ percentile ( $Q_3$ ) and the $25^{\text{th}}$ percentile ( $Q_1$ ) of the data.
Match correct choice: Step $3$ : Match the correct choice based on the definition of IQR. The problem states that the interquartile range is $15$ tickets, which directly measures variability. Therefore, the correct answer is (C) $15$ tickets.

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