Question

what would be the outlier in this set of data: 4,3,10,24,12,13,13,14,17,20

Answer 1

To determine the outlier in the data set \(4, 3, 10, 24, 12, 13, 13, 14, 17, 20\), we can use the interquartile range (IQR) method. Here’s how to do it:

1. **Order the data:**
\[ 3, 4, 10, 12, 13, 13, 14, 17, 20, 24 \]

2. **Find the quartiles:**
- The median (Q2) is the average of the 5th and 6th values:
\[
Q2 = \frac{13 + 13}{2} = 13
\]
- The lower quartile (Q1) is the median of the first half of the data:
\[
Q1 = \frac{4 + 10}{2} = 7
\]
- The upper quartile (Q3) is the median of the second half of the data:
\[
Q3 = \frac{17 + 20}{2} = 18.5
\]

3. **Calculate the interquartile range (IQR):**
\[
IQR = Q3 - Q1 = 18.5 - 7 = 11.5
\]

4. **Determine the lower and upper bounds for outliers:**
- Lower bound = \( Q1 - 1.5 \times IQR = 7 - 1.5 \times 11.5 = 7 - 17.25 = -10.25 \)
- Upper bound = \( Q3 + 1.5 \times IQR = 18.5 + 1.5 \times 11.5 = 18.5 + 17.25 = 35.75 \)

5. **Identify the outliers:**
Any data point below -10.25 or above 35.75 is considered an outlier. Looking at the data set \(4, 3, 10, 24, 12, 13, 13, 14, 17, 20\), the only outlier is **24**, as it is noticeably higher than the rest of the values in the set.

Thus, the outlier in this data set is **24**.