Question

the data set represents the number of miles mary jogged each day for the past nine days.
6, 7, 5, 0, 6, 12, 8, 6, 9
what is the outlier of the data?
○ 0
○ 6
○ 7
○ 12

Explanation:

Step1: Sort the data set

$0, 5, 6, 6, 7, 8, 9, 12$

Step2: Find median (Q2)

Median = $\frac{6+7}{2}=6.5$

Step3: Find Q1 (lower median)

Q1 = median of lower half: $\frac{5+6}{2}=5.5$

Step4: Find Q3 (upper median)

Q3 = median of upper half: $\frac{8+9}{2}=8.5$

Step5: Calculate IQR

IQR = $Q3 - Q1 = 8.5 - 5.5 = 3$

Step6: Set outlier bounds

Lower bound: $Q1 - 1.5\times IQR = 5.5 - 1.5\times3 = 1$
Upper bound: $Q3 + 1.5\times IQR = 8.5 + 1.5\times3 = 13$

Step7: Identify outlier

Values outside $[1,13]$: $0$ is below 1, $12$ is within bounds.

Answer:

0