Midpoint, market ratio, mean, median, merit bonus – I don’t know what it is with “m” words in compensation, but there are a lot of them and it can get confusing. Let’s try to simplify things by breaking down the difference between two commonly confused words: mean and median.
how to calculate The Mean
First, let’s talk about the mean. The mean is the same thing as the average. It is the result of dividing the sum of two or more values by the number of values. So (a+b+c)/3 = the mean or average.
Let’s take a real life example. Say you have five employees in the accounting department and their annual salaries are:
The sum of these five salaries is $264,000. Divide that by the number of data points (five) and you get an average or mean salary of $52,800.
How to calculate The Median
The median is the middle value of a series of values laid out in numerical order. It is the middle point of the data set; it’s also known as the midpoint. Half of the values in your list will be less than the median, and half will be higher than the median. Let’s use the example of the accounting department above to determine the median.
The first step in determining a median is to put the values in order from lowest to highest. So our list of data would look like this:
Since this is a small list, we can easily see that the value of $55,000 is the middle value of the set. Half of the values (two in this example) are lower than $55,000 and half of them (two) are higher than $55,000. So, $55,000 is the median or midpoint of the salaries of our accounting department.
The median, or the midpoint, is a very common term used in compensation and preferred to the mean (we’ll talk about why in a minute).
The Difference Between Mean and Median
Now if we compare our median value of $55,000 to the mean we calculated of $52,800, you might be thinking those numbers are pretty close so what’s the big difference? That’s an excellent question.
If the values in the data set are not too spread out, like in our example, the mean and the median may not be very different. However, this is often not the case, so it’s important to understand the difference. Let’s take an example where the mean and the median of a set of values are different. Let’s use the same data values as above, but add a few more. Let’s add in the salaries of two recent hires right out of school at $40,000 each and another new hire at $50,000. And let’s also add in the salaries of two very tenured accountants who have been with the company for 20 years, each at $88,000 and a controller at $120,000. Now let’s see what we get when we do the math.
The mean of this new data set would be the sum of the values ($690,000) divided by the number of values (11). This gives you a mean or average salary for the accounting department of $62,727.
Now for the median of this new data set. First, we lay them out in order from lowest to highest:
The middle of this set is the 6th value: $55,000. That is the midpoint and the median pay for the accounting department. That is 12 percent less than the average we calculated earlier, which is a significant difference.
Advantages of Using the Median
When setting compensation, it is generally better to use the median as opposed to the mean for a simple reason: the mean or average is very sensitive to outliers (abnormally low or high values), while the median is much less affected by outliers.
Let’s use our same example as above but throw in a very high value of $300,000, let’s say for the CFO. Our mean is now $82,500 – almost $20,000 more than the mean without the CFO. But the new median is $57,000 (halfway between the values of $55,000 and $59,000). This is only a tiny bit higher than it was without the CFO, and a huge difference from the mean. In most compensation scenarios, we are interested in knowing what pay is common or typical.
In this accounting department, $83,916 is not typical. It’s an artificially high number due to the outlier of the CFO. On the other hand, the addition of the CFO’s salary barely impacted the median – it increased by only $2000. So when dealing with outliers or abnormal values, the median is a much better indicator of typical or common pay.
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