Boxplots and bar graphsI'm studying for the GRE and came across several questions that I was unable to answer in a practice booklet, even after looking at the answer and trying to work backwards, and searching google and other sites for helpful hints. I think I am missing a fundamental understanding or useful heuristic for solving many of these problems; any advice would be greatly appreciated as my exam is Monday (Aug 1st).1. Eight hundred insects were weighed, and the resulting measurements, in milligrams, are summarized in the boxplot below.If the 80th percentile of the measurements is 130 milligrams, about how many measurements are between 126 milligrams and 130 milligrams?I calculated the range (41), the quartiles(Q1=114, Q2=118, Q3=126), and the IQR (12), but I'm confused about the question. If the 80th percentile (so 80% of the measurements?) is at 130, then 640 are within this percentile. I'm not sure if this is true and even if it is, where to go from here. Each quartile is 25% of the data, correct? So from 126 to 146 must contain 25%, or 200 measurements? (1-.8)(200) = 40, but conceptually I'm lacking what that means.2.This question refers to the following graph:(a) In 2003 the family used a total of 49 percent of its gross annual income for two of the categories listed. What was the total amount of the family’s income used for those same categories in 2004 ?My confusion lies with the fact that I can't seem to find any combination of two categories that add up to 49%. Plus, it seems that the total % expenditure in each year is 101%. The chart is not 100% accurately drawn, but even being very liberal in measuring there seems to be a discrepancy.

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Boxplots and bar graphsI&#039;m studying for the GRE and came across several questions that I was unable to answer in a practice booklet, even after looking at the answer and trying to work backwards, and searching google and other sites for helpful hints. I think I am missing a fundamental understanding or useful heuristic for solving many of these problems; any advice would be greatly appreciated as my exam is Monday (Aug 1st).1. Eight hundred insects were weighed, and the resulting measurements, in milligrams, are summarized in the boxplot below.If the 80th percentile of the measurements is 130 milligrams, about how many measurements are between 126 milligrams and 130 milligrams?I calculated the range (41), the quartiles(Q1=114, Q2=118, Q3=126), and the IQR (12), but I&#039;m confused about the question. If the 80th percentile (so 80% of the measurements?) is at 130, then 640 are within this percentile. I&#039;m not sure if this is true and even if it is, where to go from here. Each quartile is 25% of the data, correct? So from 126 to 146 must contain 25%, or 200 measurements? (1-.8)(200) = 40, but conceptually I&#039;m lacking what that means.2.This question refers to the following graph:(a) In 2003 the family used a total of 49 percent of its gross annual income for two of the categories listed. What was the total amount of the family’s income used for those same categories in 2004 ?My confusion lies with the fact that I can&#039;t seem to find any combination of two categories that add up to 49%. Plus, it seems that the total % expenditure in each year is 101%. The chart is not 100% accurately drawn, but even being very liberal in measuring there seems to be a discrepancy.

Trey Ross · Accepted Answer

For the first problem you’ve shown that you have the tools that you need; you just haven’t recognized how they apply. To say that the 80th percentile is at 130 mg is to say that 80% of the measurements are at or below 130 mg -- to the left of the 130 mg mark in the picture. Q3 gives you the 75th percentile: 75% of the measurements are at or below 126 mg, or to the left of the 126 mg mark in the picture. The measurements lying between 126 and 130 mg are inside the leftmost 80% but outside the leftmost 75%, so they make up 5% of the total, and 5% of 800 measurements is 40 measurements.Alternatively, you could work from your observation that 640 of the measurements are at or below 130 mg. (That’s not 640 measurements within the 80th percentile, however: it’s 640 measurements within the first 80 percentiles altogether.) In exactly the same way you can calculate that 75%, or 600, of the 800 measurements are at or below 126 mg. Thus, 640−600=40 measurements must lie between 126 and 130 mg.In the second question, Savings (25%) plus Mortgage, Insurance, &amp;amp; Property Taxes (24%) amounted to 49% in 2003; this doesn’t seem to require any generosity of interpretation of the graph. In 2004 those items come to 12+27=39% of $45,000, or $17,550.

Boxplots and bar graphs I'm studying for the GRE and came across several questions that I was unabl

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