Given the data set: 5, 10, 12, 14, 18, 60

Question

Which of the following statements is true regarding this data?

A
No outliers exist

B
The value 5 is the outlier.

C
Multiple outliers exist.

D
The value 60 is the outlier

Answer 1

To determine if there are outliers in the given data set (5, 10, 12, 14, 18, 60), we can use the interquartile range (IQR) method.

1. Arrange the data: The data is already in order: 5, 10, 12, 14, 18, 60.

2. Find Q1 (first quartile) and Q3 (third quartile):

   • Q1 is the median of the first half (5, 10, 12): Q1 = 10.
   • Q3 is the median of the second half (14, 18, 60): Q3 = 18.

3. Calculate the IQR: \[ \text{IQR} = Q3 - Q1 = 18 - 10 = 8. \]

4. Determine the lower and upper bounds for outliers:

   • Lower bound: \( Q1 - 1.5 \times \text{IQR} = 10 - 1.5 \times 8 = 10 - 12 = -2 \).
   • Upper bound: \( Q3 + 1.5 \times \text{IQR} = 18 + 1.5 \times 8 = 18 + 12 = 30 \).

5. Identify outliers:

   • Any value below -2 or above 30 is considered an outlier.
   • In the given data set, 60 is above 30.

Thus, the correct statement regarding the outliers in the data set is:

D: The value 60 is the outlier.