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
To determine outliers, we can use the rule of thumb, which states that data values below $Q_1-1.5 \times \text{IQR}$ or above $Q_3+1.5 \times \text{IQR}$ are considered outliers.
First, let's calculate the quartiles and the interquartile range (IQR):
Quartiles:
$Q_1$ (25th percentile)$=29$
$Q_3$ (75th percentile)$=34$
Interquartile range (IQR):
$\text{IQR}=Q_3-Q_1=34-29=5$
Now we can calculate the thresholds for outliers:
Lower threshold$=Q_1-1.5 \times \text{IQR}=29-1.5 \times 5=21.5$
Upper threshold$=Q_3+1.5 \times \text{IQR}=34+1.5 \times 5=41.5$
Outliers:
A. $2$ (below lower threshold, so outlier)
B. $27$ (between lower and upper thresholds, so not outlier)
C. $34$ (not an outlier)
D. $96$ (above upper threshold, so outlier)
Therefore, the outliers are A. $2$ and D. $96$.