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. A. 2 B. 27 C. 34 D. 96
The median of the data set is 32.
To determine if a data value is an outlier, we need to calculate the interquartile range (IQR) and then use it to find the lower and upper bounds.
IQR = Q3 - Q1
Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half.
Q1 = 27 and Q3 = 34
IQR = 34 - 27 = 7
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
Any data value that is less than the lower bound or greater than the upper bound is considered an outlier.
Therefore, the outliers in this data set are:
A. 2
D. 96