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 1336 times ]
Range = 146 - 105 = 41

Attachment:

Eight hundred insects were weighed, and the resulting measurements2.png [ 12.95 KiB | Viewed 1332 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 1338 times ]
So, the number of measurements are BETWEEN 126 mg and 130 mg = 640 - 600 = 40

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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