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

Question

Which of the following statements is true regarding this data?

A
The value 60 is the outlier

B
No outliers exist

C
Multiple outliers exist.

D
The value 5 is the outlier.

Answer 1

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

First, we need to calculate the quartiles:

1. Order the data: The data is already sorted: 5, 10, 12, 14, 18, 60.

2. Determine Q1 (the first quartile): This is the median of the first half of the data (5, 10, 12). The median here is 10.

3. Determine Q3 (the third quartile): This is the median of the second half of the data (14, 18, 60). The median here is 18.

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

5. Determine the lower and upper bounds to identify outliers:

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

An outlier is a value that is below the lower bound or above the upper bound. In this case:

• The lower bound is -2, and there are no values below this.
• The upper bound is 30, and the value 60 is above this bound.

Thus, the value 60 is indeed an outlier, while the other values are within the acceptable range.

Given the options, the correct statement is:

A: The value 60 is the outlier.