Carcass wrote:
Eight hundred insects were weighed, and the resulting measurements, in milligrams, are summarized in the boxplot below.
Attachment:
The attachment #GREexcercise Eight hundred insects were weighed.jpg is no longer available
(a) What are the range, the three quartiles, and the interquartile range of the measurements?
(b) If the 80th percentile of the measurements is 130 milligrams, about how many measurements are between 126 milligrams and 130 milligrams?
(a) range=41, Q_1 =114, Q_2 =118, Q_3 =126, interquartilerange=12 (b) 40 measurements
Math Review
Question: 5
Page: 297
Difficulty: medium
(a) What are the range, the three quartiles, and the interquartile range of the measurements? Attachment:
Eight hundred insects were weighed, and the resulting measurements1.png [ 12.69 KiB | Viewed 22596 times ]
Range = 146 - 105 = 41
Attachment:
Eight hundred insects were weighed, and the resulting measurements2.png [ 12.95 KiB | Viewed 22584 times ]
The three quartiles are:
Q1 = 114, Q2 = 118, Q3 = 126
The interquartile range = (3rd quartile) - (1st quartile)
= 126 - 114
= 12
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(b) If the 80th percentile of the measurements is 130 milligrams, about how many measurements are between 126 milligrams and 130 milligrams?80th percentile of the measurements is 130 milligramsThis means 80% of the measurements are LESS than 130 mg
80% of 800 = 640
So, 640 measurements are LESS than 130 mg
KEY CONCEPT: The 3rd quartile (Q3) is the same as the 75th percentile. Q3 = 126
So, 75% of the measurements are LESS than 126 mg
75% of 800 = 600
So, 60 measurements are LESS than 126 mg
We get:
Attachment:
Eight hundred insects were weighed, and the resulting measurements3.png [ 24.75 KiB | Viewed 22578 times ]
So, the number of measurements are BETWEEN 126 mg and 130 mg = 640 - 600 = 40
Cheers,
Brent
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Brent Hanneson - founder of Greenlight Test Prep