Question

question 4 (multiple choice worth 10 points)
(01.02h mc)

the table given shows the length, in feet, of dolphins at an aquarium.

\

$$\begin{array}{|c|c|c|c|c|c|c|c|} \\hline 3 & 15 & 30 & 19 & 11 & 18 & 17 & 12 \\\\ \\hline \\end{array}$$

are there any outliers in the data?

• there is an outlier at 3 feet.
• there is an outlier at 30 feet.
• there are outliers at 3 and 30 feet.
• there are no outliers.

Explanation:

Order the data and find quartiles

$$ \text{Ordered data: } 3, 11, 12, 15, 17, 18, 19, 30 $$

$$ n = 8 $$

$$ Q_1 = \frac{11 + 12}{2} = 11.5 $$

$$ Q_3 = \frac{18 + 19}{2} = 18.5 $$

Calculate IQR and outlier boundaries

$$ \text{IQR} = Q_3 - Q_1 = 18.5 - 11.5 = 7 $$

$$ \text{Lower Bound} = Q_1 - 1.5 \times \text{IQR} = 11.5 - 1.5(7) = 1 $$

$$ \text{Upper Bound} = Q_3 + 1.5 \times \text{IQR} = 18.5 + 1.5(7) = 29 $$

Identify outliers

$$ \text{Outliers } < 1 \text{ or } > 29 $$

$$ 30 > 29 \implies 30 \text{ is an outlier} $$

$$ 3 > 1 \implies 3 \text{ is not an outlier} $$

Answer:

• There is an outlier at 3 feet.
• There is an outlier at 30 feet. (Correct answer)
• There are outliers at 3 and 30 feet.
• There are no outliers.