Question

The data set shows the numbers of pages in the books on a reading list.

71, 96, 110, 112, 114, 114, 121, 127, 135, 175, 180


Which data values are outliers?

Select each correct answer.

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Responses

a 71
a 71

b 96
b 96

c 175
c 175

d 180

Answer 1

To determine which values are outliers in the given data set, we can use the Interquartile Range (IQR) method. Here are the steps to follow:

1. **Arrange the data in ascending order**: The data is already in order:
\[ 71, 96, 110, 112, 114, 114, 121, 127, 135, 175, 180 \]

2. **Find the first (Q1) and third quartiles (Q3)**:
- There are 11 data points.
- Q1 is the median of the first half of the data:
- First half: \( 71, 96, 110, 112, 114 \) (5 numbers)
- Median of the first half: \( 110 \) (the third number)
- Q3 is the median of the second half of the data:
- Second half: \( 114, 121, 127, 135, 175, 180 \) (5 numbers)
- Median of the second half: \( 135 \) (the third number)

3. **Calculate the IQR**:
\[ \text{IQR} = Q3 - Q1 = 135 - 110 = 25 \]

4. **Determine the outlier boundaries**:
- Lower boundary:
\[ Q1 - 1.5 \times \text{IQR} = 110 - 1.5 \times 25 = 110 - 37.5 = 72.5 \]
- Upper boundary:
\[ Q3 + 1.5 \times \text{IQR} = 135 + 1.5 \times 25 = 135 + 37.5 = 172.5 \]

5. **Identify outliers**:
- Any values below 72.5 or above 172.5 qualify as outliers.
- Check the data:
- 71 is less than 72.5 (outlier)
- 180 is greater than 172.5 (outlier)

So the outliers in this data set are **71** and **180**.

The correct answers are:
- a 71
- d 180