When you’re comparing a set of numbers, should you rely on the average or median? The definition may sound the same, but it really isn’t.
I apologize for the math lesson in advance. If you’re like me, the less you have to think about math, the better. But to the extent that this involves math and language, I thought it was important to explain the difference between average or median.
If you listen to the description of the two terms, you might think they were the same thing. But one of them can help you get a more clear picture by removing the extremes from the equation.
For the purposes of example, let’s say we have five brand new cars. Just for fun, I went to the Chevrolet website. Ford enthusiasts, I simply chose an automaker at random; don’t take offense.
I picked five different models of Chevrolet SUV: The Trax, the Trailblazer, the Equinox, the Blazer and the Tahoe. If you know your SUVs, you probably know the Tahoe has the largest starting price. The Trax has the lowest.
The starting prices are, in order: $23,300, $27,125, $30,575, $41,470 and $73,825.
I imagine more people know what an average is than a median. But here’s why the difference is very important.
To determine the average, you would take the five values, add them up, then divide by five. That would give you an average price of $39,259. Let’s say your budget would allow you to spend no more than $35,000. If you go by the average price for a brand new SUV, an SUV is clearly out of the question.
You may also hear the term mean. The mean is another word for average.
Some people might try to oversimplify things by simply adding up the highest and lowest values and dividing by two. Hey, it certainly saves you some work when it comes to math.
Unfortunately, that does not give you the average. In fact, that method would give you a result of $48,562.50, which is even further off from either the average or median. If you’re trying to look for a quick way to determine if an SUV might fit your budget, you’d feel even more hopeless.
To determine the median, however, you simply take the middle value. In this case, the middle value is $30,575. That median price of less than $31,000 tells you an SUV is definitely within your budget. In fact, three of the five fit your budget. The only question is whether any of those three have all of the bells and whistles you’d consider essential.
The median is essentially the value that falls at the midpoint between the lowest value and the highest value.
The median can often be the better choice to look at, particularly when it comes to comparing prices, because it eliminates a very high top price or a very low bottom price that will otherwise distort an average price.
When you have an odd number of values, you literally pick the number in the middle. If you have three values, it’s the second. If you have nine, it’s the fifth.
If you have an even number of values, well, you have to determine the average of the two middle numbers. Let’s say there were four values instead of five. You’d take the two middle values — the second and third — add them, then divide by two. That would give you the price that falls directly between the lowest half of prices and the highest price of values. If you had 12 values, you’d use the average of the fifth and sixth values.
Since choosing the median can sometimes require determining an average, it’s important to know and understand what’s different about each and why the median might give you the better picture.