The list shows the temperature, in °F at noon during a 9-day period.

Question

76, 71, 74, 77, 75, 71, 87, 77, 75

Which temperature is an outlier?

Answer 1

To determine if there is an outlier in the given set of temperatures, we can use the IQR (Interquartile Range) method.

1. Sort the Data:
   The temperatures in sorted order:

   • 71, 71, 74, 75, 75, 76, 77, 77, 87

2. Find the First Quartile (Q1) and Third Quartile (Q3):

   • Q1 (the median of the first half) is the average of the 2nd and 3rd numbers:
     Q1 = (71 + 74) / 2 = 72.5
   • Q3 (the median of the second half) is the average of the 7th and 8th numbers:
     Q3 = (77 + 77) / 2 = 77

3. Calculate the Interquartile Range (IQR):

   • IQR = Q3 - Q1 = 77 - 72.5 = 4.5

4. Determine the Outlier Boundaries:

   • Lower Boundary = Q1 - 1.5 * IQR = 72.5 - 1.5 * 4.5 = 72.5 - 6.75 = 65.75
   • Upper Boundary = Q3 + 1.5 * IQR = 77 + 1.5 * 4.5 = 77 + 6.75 = 83.75

5. Identify Outliers:

   • Any temperature below 65.75 or above 83.75 is considered an outlier.

From the list, 87°F is the only temperature that falls above the upper boundary of 83.75. Thus, 87°F is the outlier.