Good morning & happy Monday!
“Statistics are like a bikini. What they reveal is interesting. But what they hide is vital.”
Aaron Levenstein, former business professor
Last week I addressed math, today I am going to jump into statistics. I can tell you are excited! 😉
My wife and I were talking about statistics the other day. I find the topic fascinating; she finds it torturous.
Hopefully today’s memo will not cause you to go into a deep sleep … I’ll try to make this memo as interesting and informative as possible without getting too deep into the weeds.
What does “average” even mean? Well, there are all sorts of ways to calculate this, and here lies where statistics can be so easily manipulated to tell whatever story the storyteller wants to tell.
There are 3 main statistical ways to calculate “average.”
- Mean
- Median
- Mode
Let’s use annual income as an example. Let’s say we are studying 10 people who have the following annual income:
- $15,000/year
- $20,000/year
- $30,000/year
- $30,000/year
- $40,000/year
- $50,000/year
- $70,000/year
- $100,000/year
- $250,000/year
- $1,000,000/year
What is the average salary of this group?
Well, it depends on which method we use: mean, median, or mode.
Mean = add the numbers together and divide by the number of numbers. In this case, we would add $15,000 + $20,000 + $30,000 + $30,000 + $40,000 + $50,000 + $70,000 + $100,000 + $250,000 + $1,000,000 to get $1,605,000 (this is the total income of all the 10 people added together). Then we would simply divide that figure by 10 (the number of people in the group) to get $160,500. The “average” salary of this group is $160,500 using the mean average.
Median = arrange the numbers in order (smallest to greatest) and pick the middle number. In this case, we would look at income #5 at $40,000/year and income #6 at $50,000/year and determine the “average” income is between the 2 of them at $45,000/year. The “average” salary of this group is $45,000 using the median average.
Mode = the value that occurs the most often. In this case, we see that the only income that is repeated is $30,000, so that is the mode. The “average” salary of this group is $30,000 using the mean average.
How crazy is this?!?! In this hypothetical scenario if I said the average income was $160,500 I would be correct. I would also be correct if I said the average income is $45,000/year. Yet I still would be correct stating that the average income of the group is $30,000/year.
See how easy it is to manipulate statistics to make whatever point I want to make?
Let’s say I want to attract a high-profile business to the area I might make a statement like, “The average income is over $160,000/year here.” I’m not wrong.
If I am running for a political office and I’m trying to get people to vote for me I might say something along the lines of, “The average income here is only $30,000/year and we can do better.” … I would not be lying.
In this example the individual who makes $1,000,000/year has dramatically altered the mean, but has much less effect on the median, and no effect on the mode. If we took out that person all together the mean would move to from $160,500 to $67,222/year income, the median would be $40,000 instead of $45,000, and the mode would be unaffected staying at $30,000.
Does your head hurt yet? 😉
I have a love / hate relationship with statistics. They are so incredibly valuable but they can also so easily be used to deceive.
Let’s look at one more hypothetical example, this time using finance.
Let’s say a stock has had the following annual returns over the last 10 years (again, completely hypothetical):
- Year 1 = +5.00%
- Year 2 = +3.50%
- Year 3 = -15.50%
- Year 4 = +18.25%
- Year 5 = +3.50%
- Year 6 = +26.75%
- Year 7 = +16.50%
- Year 8 = +4.75%
- Year 9 = -6.25%
- Year 10 = +14.50%
What’s my average?
By the mean it’s 7.10% (add all the numbers together and divide by the 10 years)
By the median it’s 4.875% (put all the numbers in order and pick the middle # … in this case #5 is 4.75% and #6 is 5.00% so the median is the figure between the 2)
By the mode it’s 3.50% (the figure that occurs the most … in this case it’s the only number that is repeated so it’s the mode average)
So, depending on how you look at it (calculate it) you could say this investment has averaged 7.10%, or 4.875%, or 3.50% over the last 10 years.
What story are you looking to tell? Statistics can oftentimes be found to back up that story! Kinda cool and kinda scary all at the same time!
My main point in bringing this up is to arm you with information. I believe the more informed we are the better an investor we will be (not to mention a more informed consumer, voter, etc.). I seek to arm you with information! 😊
I hope this email has been helpful in providing you with some perspective in an area that can be so unbelievably confusing. I also hope I have not put you to sleep 😉 It’s an incredible honor to partner with you … I hope it’s a wonderful week ahead!