Distribution Question

[baily106]

Hello,

I am referring to question #5 on page 297 of The Official Guide Book. Question #5 has two parts a and b. Could you please explain both parts? The question asks a) what are the range, the three quartiles, and the interquartile range of the measurements? The second question asks b) if the 80th percentile of the measurements is 130 milligrams, about how man measurements are between 126 milligrams and 130 milligrams.

Unfortunately, I couldn't pull the diagram on here.

Thanks.

[tommywallach]

The range is 41, because the lines stretch from 105 to 146.

The quartiles are simply defined by where the lines of the box plot are (this is just a rule). So the first quartile is at 114 (the leftmost line of the box). The second is at 118 (the middle line in the box). The third is at 126 (the rightmost line of the box).

The interquartile range is defined as the distance between the first quartile and the third quartile. In this case, that's 12.

The 80th percentile is 130. We already know that the 75th percentile (Q3) is at 126. So 5% of the data set falls in that range. 5% of 800 (we are told up top that 800 insects were weighed) is 40.

Hope that helps!

-t

[baily106]

It does; thank you.

[tommywallach]

No problem!