Question

(01.02h mc)
the table given shows the length, in feet, of dolphins at an aquarium.
7 13 15 28 11 19 9 15
are there any outliers in the data?
there is an outlier at 28 feet
there is an outlier at 7 feet
there are outliers at 7 and 28 feet
there are no outliers

Explanation:

Step1: Sort the data set

$7, 9, 11, 13, 15, 15, 19, 28$

Step2: Find median (Q2)

Median = $\frac{13 + 15}{2} = 14$

Step3: Find Q1 (lower median)

Lower half: $7, 9, 11, 13$; Q1 = $\frac{9 + 11}{2} = 10$

Step4: Find Q3 (upper median)

Upper half: $15, 15, 19, 28$; Q3 = $\frac{15 + 19}{2} = 17$

Step5: Calculate IQR

IQR = $Q3 - Q1 = 17 - 10 = 7$

Step6: Find outlier bounds

Lower bound: $Q1 - 1.5\times IQR = 10 - 1.5\times7 = -0.5$
Upper bound: $Q3 + 1.5\times IQR = 17 + 1.5\times7 = 27.5$

Step7: Identify outliers

Only 28 > 27.5, so 28 is an outlier.

Answer:

There is an outlier at 28 feet