Mrs. Jones recorded the time, in minutes, she spends reading each day for two weeks. The results are shown. What is the IQR for each week?
Week 1
81 50 63 58 39 72 104
Week 2
62 54 110 72 68 34 79
A.
The IQR for Week 1 is 65, and the IQR for Week 2 is 76.
B.
The IQR for Week 1 is 63, and the IQR for Week 2 is 68.
C.
The IQR for Week 1 is 50, and the IQR for Week 2 is 54.
D.
The IQR for Week 1 is 31, and the IQR for Week 2 is 25.
I answered this earlier today.
What is IQR?
To find the IQR (Interquartile Range) for each week, we need to find the values of Q1 and Q3 first.
Step 1: Sort the data in ascending order.
Week 1: 39 50 58 63 72 81 104
Week 2: 34 54 62 68 72 79 110
Step 2: Find Q1 (the lower quartile) and Q3 (the upper quartile).
Q1: The median of the lower half of the data.
Week 1: Q1 = 58
Week 2: Q1 = 54
Q3: The median of the upper half of the data.
Week 1: Q3 = 81
Week 2: Q3 = 79
Step 3: Calculate the IQR.
IQR = Q3 - Q1
Week 1: IQR = 81 - 58 = 23
Week 2: IQR = 79 - 54 = 25
Therefore, the correct answer is D. The IQR for Week 1 is 23, and the IQR for Week 2 is 25.