I abhor averages. I like the individual case. A man may have six meals one day and none the next, making an average of three meals per day, but that is not a good way to live.
~ Louis D. Brandeis
I hope you’ll forgive me for the little double entendre in the title of this post. Being a writer and a poet I love playing with words and I just couldn’t help myself.
So let’s explore and understand what is the mean, how it compares to the median and thus let’s find out what the median is and also, is it important or even useful for us to know the mean in day to day life other than if we are mathematicians or scholars.
Okay, so what is the mean? In the easiest term possible, the mean is just another name for average in mathematics and statistics.
For example, when I go to the Oxford Dictionary for the meaning this is what I find: the quotient of the sum of several quantities and their number; an average:
See how they complicate thing? I mean really, what does that mean “the quotient..” Well, let’s see what quotient means. A quotient is a term used in math that is basically just the result when you divide one thing by another.
Okay, so let’s say it another way. The mean is the result of adding the sum of several things and then divided by the number of things. An average as mentioned before.
Let’s look at an example. Let’s say there are 10 people in the room and we want to know the “mean” or average of their age. We need to know how many people there are as well as their respective ages.
The ages of the 10 people is as follows: 12, 9, 18, 14, 17, 16, 13, 15, 11 and 99. So adding all their ages together we get 22.4. Now that is the mean of their ages, but do you see a problem with this? The problem is that a much higher or much lower number can skew the result or the “mean” upwards or downwards respectively. In our example, the mean has been skewed upwards. If we exclude the outlier the 99 year old in a room of teens we get a more realistic and appropriate mean.
When we add the ages of the first 9 people and divide by 9 our mean is a more accurate 13.89.
When you have numbers that have large outliers on either the high or low side you want to use what is called the median instead of the mean as the median compensates for outliers that tend to skew the average or “mean” number.
The median is useful and more accurate but much harder to formulate for and as such is used primarily in statistics. I’m not going into the idea of a “median” here as it is above my pay grade, and frankly when reading about it at Wikipedia (go there if you want more on it), my eyes glaze over 🙂
For our purposes, the mean or average is usually sufficient for figuring… well, averages out. But it doesn’t give a truly realistic picture of the average in all situations.
Here is another example. Let’s say Warren Buffett moves into my middle class neighbourhood and let’s say the average household income of my neighbourhood is $50k a year as determined by the mean of the 10 households in the ‘hood. Now we add in Buffett who let’s say earns $100 million a year (I’m just guessing with the numbers, play along). Well now we have the mean or average being around $9 million per year. Yet the probability of you earning that salary in my neighbourhood is next to zero. So the median might give a number like $50k in this situation to compensate for Buffett’s billions.
So we can and should use the average or mean in our daily lives. Usually we won’t encounter huge outliers on either end in our day to day uses that will skew the results.
We might want to figure out what the mean number of kids there are per couple in our circle of 15 friends. We might want to figure out what the mean salary amongst our friends or co-workers is. All these things are unlikely to have outliers to mess with the mean.
Other examples we might use on a daily basis could be to determine the average number of pounds of weight loss amongst the 7 of us who attend weekly weigh-ins together.
The important thing is to remember that there is a chance that the mean or an average of a bunch of numbers might be skewed if their are outliers. This is important to know especially when looking at making big investments or purchases.
If you’re looking to buy a house in a good neighbourhood and the houses are priced at around $200k and yet your realtor is telling you that the average income in the neighbourhood is $500k a year, then you know there must be an outlier or two skewing that income upwards.
Same if you want to start investing with a group of people. If they say that the average interest earned was $1,000 per year out of the 12 people in the club, that could be a good average, or it could mean that 11 people lost their shirts and one person made a mint. This is why understanding means and averages and when they don’t really give you a true picture is important.
I hope you get my meaning 😉 I say what I mean and I mean what I say without trying to be mean. LOL, okay, I’m outta here. Thanks for you patience!