Question

the list shows the temperature, in °f, at noon during a 9-day period.
76, 71, 74, 77, 75, 71, 87, 77, 75
which temperature is an outlier? enter the answer in the box.
□ °f

Explanation:

Step1: Order the data

First, we order the temperature data: \( 71, 71, 74, 75, 75, 76, 77, 77, 87 \)

Step2: Find Q1 and Q3

The median (middle value) of the data set (since there are 9 values, the 5th value) is \( 75 \).

• The lower half (values below the median) is \( 71, 71, 74, 75 \). The median of this lower half (Q1) is the average of the 2nd and 3rd values: \( \frac{71 + 74}{2} = 72.5 \)
• The upper half (values above the median) is \( 76, 77, 77, 87 \). The median of this upper half (Q3) is the average of the 2nd and 3rd values: \( \frac{77 + 77}{2} = 77 \)

Step3: Calculate IQR

The interquartile range (IQR) is \( Q3 - Q1 = 77 - 72.5 = 4.5 \)

Step4: Determine outlier boundaries

• Lower bound: \( Q1 - 1.5 \times IQR = 72.5 - 1.5 \times 4.5 = 72.5 - 6.75 = 65.75 \)
• Upper bound: \( Q3 + 1.5 \times IQR = 77 + 1.5 \times 4.5 = 77 + 6.75 = 83.75 \)

Step5: Identify the outlier

We check which temperature is outside the bounds \( 65.75 \) to \( 83.75 \). The temperature \( 87 \) is greater than \( 83.75 \), so it is an outlier.

Answer:

\( 87 \)