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.
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.