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Answer:
A) 8.5 miles per gallon
Step-by-step explanation:
Given
[tex]x = \{12\ 13\ 15\ 16\ 16\ 17\ 18\ 18\ 19\ 19\ 20\ 20\ 22\ 23\ 24\ 26\ 26\ 27\ 27\ 29\}[/tex]
[tex]n = 20[/tex]
Required
The IQR
This is calculated as:
[tex]IQR = Q_3 - Q_1[/tex]
Calculate [tex]Q_1[/tex]
[tex]Q_1 = \frac{1}{4}(n + 1)th[/tex]
[tex]Q_1 = \frac{1}{4}(20 + 1)th[/tex]
[tex]Q_1 = \frac{1}{4}(21)th[/tex]
Remove bracket
[tex]Q_1 = 5.25th[/tex]
This means that:
[tex]Q_1[/tex] is the mean of 5th and 6th item
From the given data:
[tex]5th \to 16[/tex]
[tex]6th \to 17[/tex]
So, we have:
[tex]Q_1 = \frac{1}{2}(16 + 17)[/tex]
[tex]Q_1 = \frac{1}{2}(33)[/tex]
[tex]Q_1 = 16.5[/tex]
[tex]Q_1 = 16.25[/tex]
Calculate [tex]Q_3[/tex]
[tex]Q_3 = \frac{3}{4}(n + 1)th[/tex]
[tex]Q_3 = \frac{3}{4}(20 + 1)th[/tex]
[tex]Q_3 = \frac{3}{4}(21)th[/tex]
Remove bracket
[tex]Q_3 = 15.75th[/tex]
This means that:
[tex]Q_3[/tex] is the mean of 15th and 16th item
From the data:
[tex]15th \to 24[/tex]
[tex]16th \to 26[/tex]
So:
[tex]Q_3 = \frac{1}{2}(24 + 26)[/tex]
[tex]Q_3 = \frac{1}{2}(50)[/tex]
[tex]Q_3 = 25[/tex]
Recall that:
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR = 25 -16.5[/tex]
[tex]IQR = 8.5[/tex]