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
Week 2
81 50 63 58 39 72 104
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.
can someone give the answer for the entire test
its D
To find the IQR (Interquartile Range) for each week, we first need to determine the upper quartile (Q3) and the lower quartile (Q1) for each week.
To find Q1 and Q3, we need to arrange the data in each week in ascending order.
Week 1 data (in ascending order): 39 50 58 63 72 81 104
Week 2 data (in ascending order): 34 54 58 62 68 72 79 110
Next, we calculate Q1 and Q3.
For Week 1:
Q1 = The median of the lower half of the data = (58 + 63) / 2 = 120 / 2 = 60
Q3 = The median of the upper half of the data = (81 + 104) / 2 = 185 / 2 = 92.5
For Week 2:
Q1 = The median of the lower half of the data = (54 + 58) / 2 = 112 / 2 = 56
Q3 = The median of the upper half of the data = (72 + 79) / 2 = 151 / 2 = 75.5
Finally, to find the IQR for each week, we subtract Q1 from Q3.
For Week 1: IQR = Q3 - Q1 = 92.5 - 60 = 32.5
For Week 2: IQR = Q3 - Q1 = 75.5 - 56 = 19.5
So, the correct answer is D. The IQR for Week 1 is 32.5, and the IQR for Week 2 is 19.5.