Source: Official Guide Revised GRE 1st Ed. Part 8; Section 6; #13

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# The company at which Mark is employed

The company at which Mark is employed has 80 employees, each of whom has a different salary. Mark’s salary of \$43,700 is the second-highest salary in the first quartile of the 80 salaries. If the company were to hire 8 new employees at salaries that are less than the lowest of the 80 salaries, what would Mark’s salary be with respect to the quartiles of the 88 salaries at the company, assuming no other changes in the salaries? The fourth-highest salary in the first quartile, The highest salary in the first quartile, The second-lowest salary in the second quartile, The third-lowest salary in the second quartile, The fifth-lowest salary in the second quartile

### 2 Explanations

3

Inmobi

Hi, are there any reference link to understand how the box plot behave when new numbers are added or removed, like the example above where 8 numbers are added? Please advice

Jun 7, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Inmobi :)

I wasn't able to find any resources that directly this aspect of boxplots. However, with a good fundamental understanding of boxplots and how they are structured, I think you'll more fully understand how they change when new points are added :)

Here are some good blog posts to check out:

Overall, boxplots are broken up into four sections, each one containing 1/4 of the data points in a set. So, we can know how many points are in each section by dividing the total number of points by 4.

There are five important points that are marked in a box plot:

1. The minimum
2. The 1st quartile
3. The median
4. The 3rd quartile
5. The maximum

The 1st quartile is the median of the lower half of the set of data, while the 3rd quartile is the median of the upper half. The median is the middle value.

So, to figure out what happens to a box plot when new values are added to a set, we need to know how many values of added and where they're added. In this practice problem, for example, the values are added to the lower end of the data. This "pushes" all of the other values to the right. We have to calculate how many values are in each section by dividing the new total by 4. And, as Chris discusses in the explanation, we can use the original information to determine where a given data point ends up when new values are added :)

I hope this helps, at least a little!

4 Chris Lele, Magoosh Tutor

Oct 11, 2012 • Comment

Vivek Sethia

Why do quartiles have salaries in increasing order? Why not decreasing? It isn't stated anywhere how exactly quartiles were made.

, Magoosh Tutor

Gravatar Kevin Rocci, Magoosh Tutor

Hi Vaibhav,

I can see how this might seem strange if you are not familiar with quartiles. An inherent part of quartiles is ordering things from least to greatest. To say that someone is in the top quartile means they are in the top quarter of salary earners, or whatever else you are looking at and measuring.

If you need to review quartiles, I recommend looking in the Official GRE book on page 273, or watching some videos on Khan Academy that cover this topic. :)

I hope this helps! :)