Question

Sean counted the number of stuffed animals available for prizes in each of the booths at a county fair. The list shows the results.

2, 23, 27, 29, 30, 32, 32, 34, 35, 96

Select all the data values that are outliers.

Answer 1

To determine the outliers in this data set, we can use the interquartile range (IQR) method.

First, we need to calculate the IQR:
- Start by arranging the data in ascending order: 2, 23, 27, 29, 30, 32, 32, 34, 35, 96.
- Find the first quartile, Q1: 2, 23, 27, 29, 30 (median = 27).
- Find the third quartile, Q3: 32, 32, 34, 35, 96 (median = 34).
- Calculate the IQR = Q3 - Q1 = 34 - 27 = 7.

To find any outliers, we need to determine the lower and upper bounds:
- Lower bound = Q1 - (1.5 * IQR) = 27 - (1.5 * 7) = 27 - 10.5 = 16.5
- Upper bound = Q3 + (1.5 * IQR) = 34 + (1.5 * 7) = 34 + 10.5 = 44.5

Now let's check which data values are outliers:
- 2: Not an outlier (within the bounds).
- 23: Not an outlier (within the bounds).
- 27: Not an outlier (within the bounds).
- 29: Not an outlier (within the bounds).
- 30: Not an outlier (within the bounds).
- 32: Not an outlier (within the bounds).
- 32: Not an outlier (within the bounds).
- 34: Not an outlier (within the bounds).
- 35: Not an outlier (within the bounds).
- 96: Outlier (above the upper bound).

Therefore, the only outlier in the given data set is 96.