If compensation data for a particular occupation is described as having quartile 1 at $50,000, this...

If compensation data for a particular occupation is described as having quartile 1 at $50,000, this means:

Group of answer choices

this type of terminology is not used to describe compensation data

one quarter of all employees make exactly $50,000

the standard deviation of one quarter of all employees is $50,000

three quarters of all employees make more than $12,500 plus benefits

one quarter of all employees make less than 50,000

Solutions

Expert Solution

Solution:

The Information provided in the given problem is Quartile 1(Q1) = $50,000 only.

Assume that there are 100 employees doing a particular occupation in a company.

We can arrange them based on their compensation data from smaller values to bigger values.

After that, find the midvalue/Median(Q2) from the arranged compensation data.

Q1, Quartile 1 is the midvalue of the 1st compensation data and the median(Q2).

Q3, Quartile 3 is the midvalue of the median(Q2) and the nth(or last) compensation data.

Now, let us go through the provided answer choices.

1. this type of terminology is not used to describe compensation data.

Wages data can be studied, analysed using quartiles, standard deviation, range, etc...So this answer is irrelevant or incorrect.

2.one quarter of all employees make exactly $50,000.

Since Q1 is given as $50,0000, this answer is true in the case of even number of employees and all their compensation data are equal to $50,000.

3. the standard deviation of one quarter of all employees is $50,000.

Only Quartile Q1 information is provided in the problem. No of employees and their mean compensation data are not known. Since standard deviation of one quarter of employees is $50,000, the deviation from the average compensation data is high.

4. three quarters of all employees make more than $12,500 plus benefits

This answer option is incorrect because compensation data are arranged from smaller values to bigger values and Q3 should be more than quartile 1(Q1).

5.one quarter of all employees make less than 50,000

Since Q1 is given as $50,0000, this answer is true in the case of odd number of employees.

Example, if there are 101 employees, then Quartile 1 is the median of the 25th and 26th employees' compensation data.

ekkarill92 answered 1 year ago

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