Geckos are lizards with specialized toe pads that enable them to easily climb all sorts of surfaces. A research team examined the adhesive properties of 7 Tokay geckos. Following are the toe-pad areas (in square centimeters, cm²) for this sample:
5.6 4.9 6.0 5.1 5.5 5.1 7.5
Which of the following ranges must a value fall outside of to be considered an outlier according to the 1.5 × IQR rule?

Question

Quizplus · Accepted Answer

To find the outlier range using the 1.5 × IQR rule, we need to first calculate the IQR (interquartile range). 
1. Arrange the data in ascending order: 
4.9, 5.1, 5.1, 5.5, 5.6, 6.0, 7.5 
2. Find the median (Q2): 
Since there are 7 data points, the median is the 4th value, which is 5.5. 
3. Divide the data into two halves: 
First half: 4.9, 5.1, 5.1, 5.5 
Second half: 5.6, 6.0, 7.5 
4. Find the median of the first half (Q1): 
Since there are 4 data points, the median is the average of the 2nd and 3rd values, which is 5.1. 
5. Find the median of the second half (Q3): 
Since there are 3 data points, the median is the 2nd value, which is 6.0. 
6. Calculate the IQR: 
IQR = Q3 - Q1 = 6.0 - 5.1 = 0.9 
7. Multiply the IQR by 1.5: 
1.5 × IQR = 1.5 × 0.9 = 1.35 
8. Determine the outlier range: 
Lower outlier limit = Q1 - 1.5 × IQR = 5.1 - 1.35 = 3.75 
Upper outlier limit = Q3 + 1.5 × IQR = 6.0 + 1.35 = 7.35

Therefore, any value that falls outside the range of 3.75 to 7.35 would be considered an outlier according to the 1.5 × IQR rule. 
So, the best choice is D.

Geckos Are Lizards with Specialized Toe Pads That Enable Them