Question

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 of 8 values: $\frac{13+15}{2}=14$

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: $Q1 - 1.5\times IQR = 10 - 1.5\times7=10-10.5=-0.5$
Upper bound: $Q3 + 1.5\times IQR = 17 + 1.5\times7=17+10.5=27.5$

Step7: Identify outliers

28 > 27.5, so 28 is an outlier; 7 > -0.5, so 7 is not an outlier.

Answer:

There is an outlier at 28 feet.