Question

10
the dot plot below gives the ages of the starting quarterbacks in a league at the beginning of the season. find the interquartile range of ages.
a) 6 years they lost a bet
b) 7 years they were celebrating retirement
c) 8 years they wanted to get on the news
d) 9 years they were showing off
e) 10 years they were extras in a movie

Explanation:

Step1: Count the total number of data points

Count all the dots in the dot - plot. There are \(n = 36\) data points.

Step2: Find the first quartile \(Q_1\)

The position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{36+1}{4}=9.25\)th value.
Counting the dots from the left, the 9th and 10th values (when ordered) are both \(24\). So \(Q_1 = 24\).

Step3: Find the third quartile \(Q_3\)

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(36 + 1)}{4}=27.75\)th value.
Counting the dots from the left, the 27th and 28th values (when ordered) are \(32\). So \(Q_3=32\).

Step4: Calculate the inter - quartile range (IQR)

The formula for \(IQR\) is \(IQR=Q_3 - Q_1\).
Substitute \(Q_1 = 24\) and \(Q_3 = 32\) into the formula: \(IQR=32 - 24\).

Answer:

\(8\) years (Option C)