Question

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

Explanation:

Step1: Order the data

First, we order the given temperatures: \(71, 71, 71, 73, 75, 75, 76, 77, 81\)

Step2: Find Q1, Q2, Q3

• The median (Q2) of 9 data points is the 5th value: \(Q2 = 75\)
• The lower half (first 4 values: \(71, 71, 71, 73\)) has a median (Q1) of \(\frac{71 + 71}{2}=71\)
• The upper half (last 4 values: \(75, 76, 77, 81\)) has a median (Q3) of \(\frac{76 + 77}{2}=76.5\)

Step3: Calculate IQR

IQR (Inter - Quartile Range) is \(Q3 - Q1=76.5 - 71 = 5.5\)

Step4: Find lower and upper fences

• Lower fence: \(Q1-1.5\times IQR=71-1.5\times5.5 = 71 - 8.25=62.75\)
• Upper fence: \(Q3 + 1.5\times IQR=76.5+1.5\times5.5=76.5 + 8.25 = 84.75\)

We check each data point. All data points except 81 are between 62.75 and 84.75. But 81 is relatively far from the other values. Also, by observing the data, most of the values are in the 70s, and 81 is higher than the rest.

Answer:

\(81\)