The boxplot below shows salaries for CPAs and Actuaries in a town. 30 40 50 60 70 80 90 100 Salary (thousands of $) Actuary CPA If a person is making the median salary for a CPA, his earning is equivalent to the salary for an Actuaries, and he is making less than % of Actuaries.

In order to answer this question, we have to know the meaning of a box plot. Boxplots are especially useful in statistical analysis and gives us a meaningful range of values. A box plot consists of 2 shapes, which are the box part and the extended lines. The short sides of the box and the vertical line in the middle of the box represent a certain percentage of the values. The vertical line in the boxplot is the median of your dataset. For example, according to the shape given in the question, the median value for CPA's is 50 and this is closer to the left side of the box. This means that the first half ogf the dataset (when ranked from the smallest to the greatest) is closer to each other. The sides of the box represent the values at the 25% and 75% of the values respectfully.

For example, if we have 100 values, we rank them in order and the 25th value corresponds to the left side of the boxplot (named first quartile), 50th value (which is also the median) corresponds the vertical line in the box and and the 75the value corresponds to the right side of the box (named third quartile).

The extended arms are calculated as accordingly: IQR=(3rd quartile value-1st quartile value). Left extended arm is first quartile-1.5*IQR and right extended arm is third quartile+1.5*IQR. However, this information is not directly related to this question.

Now, this question should seem simpler. The median salary of CPA is 50 and this is equal to left side of the Actuary boxplot, which corresponds to the 25% of actuaries. As a result, CPA median salary is less than 75% of the Actuaries (100%-25%).

MrRoyal MrRoyal · Answer 2 · 2021-09-03T23:57:21+02:00

Box plot is the use of a rectangle to represent data where the vertical sides of the rectangle represents the lower and upper quartile.

See attachment for the missing box plot.

There are 5 vertical lines in a box plot

The first represents the minimum value
The second represents the first quartile
The third represents the second quartile i.e. the median
The fourth represents the third quartile
The last represents the maximum quartile

From the CPA box plot.

The third vertical line (i.e. the median) is equivalent to the second vertical line (i.e. the first quartile) of the Actuary box plot.

25% represents the first quartile

This means that:

A person making the median salary for a CPA, his earning is equivalent to the first quartile salary for Actuaries, and he is making less than 25% of Actuaries.