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

Question

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

Select the two data values that are outliers.
A.
2

B.
27

C.
34

D.
96

Answer 1

To identify the outliers in the given data set, we can use the IQR (Interquartile Range) method. Here are the steps:

1. Order the Data: The data is already in order: 2, 23, 27, 29, 30, 32, 32, 34, 35, 96

2. Find the quartiles:

   • Q1 (the first quartile) is the median of the first half of the data.
   • Q3 (the third quartile) is the median of the second half of the data.

   The dataset contains 10 values, so:

   • The first half is: 2, 23, 27, 29, 30 (Median for Q1 is 27)
   • The second half is: 32, 32, 34, 35, 96 (Median for Q3 is 34)

   Q1 = 27, Q3 = 34

3. Calculate the IQR: IQR = Q3 - Q1 = 34 - 27 = 7

4. Determine the outlier boundaries:

   • 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

5. Identify outliers: Any value below 16.5 or above 44.5 is considered an outlier. The only values we have to check against these bounds are as follows:

   • 2 (is less than 16.5, so it is an outlier)
   • 23 (not an outlier)
   • 27 (not an outlier)
   • 29 (not an outlier)
   • 30 (not an outlier)
   • 32 (not an outlier)
   • 34 (not an outlier)
   • 35 (not an outlier)
   • 96 (is greater than 44.5, so it is an outlier)

Thus, the two outliers are:

A. 2
D. 96