(a) What are the range, the three quartiles, and the interquartile range of the measurements?



Range = 146 - 105 = 41



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 milligrams
This 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:


So, the number of measurements are BETWEEN 126 mg and 130 mg = 640 - 600 = 40

Cheers,
Brent
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Hi,

Any explanations for the 2nd question?

Thanks!

Interesting graph. What resource to use for practising such graph questions?

For b)

You can also notice that 126 = 75th percentile (Q3) and 130 = 80th percentile (given in the question).
So the difference between them (i.e. the numbers between them) is then equal to 5 percentiles and 5% of 800 = 40.

These https://greprepclub.com/forum/the-offic ... -8020.html

Regards
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thank you.This really helped clear my doubts

The answers to the questions:

The concept for the 2nd question is:
The percentile refers to the percentage of people (or measurements) below a given value.
For example, 80th percentile is 130 milligrams implies that:
80% of all measurements are lower than 130

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I have posted a detailed video on YouTube which talks about all aspects of Box and Whisker Plot.



Hope it helps!
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