Question

the first quartile of a data set is 41, and the third quartile is 57. which of these values in the data set is an outlier?

A)73
B)39
C)83
D)19

Answer 1

To identify outliers in a data set using the first quartile (Q1) and the third quartile (Q3), we can apply the interquartile range (IQR) method.

1. Calculate the IQR:
\[
\text{IQR} = Q3 - Q1 = 57 - 41 = 16
\]

2. Determine the lower and upper bounds for outliers:
- Lower bound: \( Q1 - 1.5 \times \text{IQR} \)
- Upper bound: \( Q3 + 1.5 \times \text{IQR} \)

Let's calculate these bounds:
\[
\text{Lower bound} = 41 - 1.5 \times 16 = 41 - 24 = 17
\]
\[
\text{Upper bound} = 57 + 1.5 \times 16 = 57 + 24 = 81
\]

3. Identify outliers:
Any data point below 17 or above 81 is considered an outlier.

Now, let's examine the values provided:
- A) 73 (not an outlier)
- B) 39 (not an outlier)
- C) 83 (outlier since it's greater than 81)
- D) 19 (not an outlier)

Thus, the outlier in the data set is **C) 83**.