Righty tighty, lefty loosey

[Wagtail]

No, I mean I took all 11 of our IQ scores, added them up, and divided by 11 to get the average. And I was the only one above that average. How is this possible?

Well I'm done guessing. You keep on changing (or adding) definition and criteria to your question. :confused3:

 

[check]

Well I'm done guessing. You keep on changing (or adding) definition and criteria to your question. :confused3:

The point I am trying to make is that it is indeed possible to have almost everyone "below average", as long as you have at least one person above average. (They just have to be a long ways above average.) This is especially true with small groups of numbers.

I picked a sample size of 10 (plus me) out of a hat, just to make it simple. Let's say it really was IQ scores, and the students were pretty smart, but nowhere near as smart as me. In fact I told them my IQ was over 160, which was a lie. (*More about that later.) And just to make it simple, let's say the students all had IQ scores of 130 (which would make them feel pretty good!) Adding everyone's score up, you get 10 x 130 =1300, plus my 160 = 1460. And thus the average is 1460/11 = 133 (rounded). So, everyone was below average except me!

*I actually did score over 160 when a friend who was studying the IQ test wanted to use me for practice. He was always boasting how smart he was, so I played a fun joke on him. I got hold of the scoring manual the night before, and memorized and practiced all the questions that I could ahead of time (in other words, I cheated). It was so much fun watching him get more and more upset as he scored the test and was forced to come to the conclusion that I was way, way "smarter" than him!

The truth of the matter is that he WAS indeed smarter than me, but to this day, he still doesn't know!:laughing::laughing:

Anyway, my view is that people pay WAY too much attention to the average, and mistakenly assume that it is always in the middle. (This is of course true of the Median, but not the average.)

 

[sixdogs]

Don't ask the question if you can't stand the answer.

Doug in SW IA

Never ask a question that you don't know the answer to.



And...If you don't want what you got you shouldn't have done what you did.

 

[Firemanbuck82]

The point I am trying to make is that it is indeed possible to have almost everyone "below average", as long as you have at least one person above average. (They just have to be a long ways above average.) This is especially true with small groups of numbers.

I picked a sample size of 10 (plus me) out of a hat, just to make it simple. Let's say it really was IQ scores, and the students were pretty smart, but nowhere near as smart as me. In fact I told them my IQ was over 160, which was a lie. (*More about that later.) And just to make it simple, let's say the students all had IQ scores of 130 (which would make them feel pretty good!) Adding everyone's score up, you get 10 x 130 =1300, plus my 160 = 1460. And thus the average is 1460/11 = 133 (rounded). So, everyone was below average except me!

*I actually did score over 160 when a friend who was studying the IQ test wanted to use me for practice. He was always boasting how smart he was, so I played a fun joke on him. I got hold of the scoring manual the night before, and memorized and practiced all the questions that I could ahead of time (in other words, I cheated). It was so much fun watching him get more and more upset as he scored the test and was forced to come to the conclusion that I was way, way "smarter" than him!

The truth of the matter is that he WAS indeed smarter than me, but to this day, he still doesn't know!:laughing::laughing:

Anyway, my view is that people pay WAY too much attention to the average, and mistakenly assume that it is always in the middle. (This is of course true of the Median, but not the average.)

"Average" is a non-statistical term since there are many types of averages. People often use "average" when they really mean "arithmetic mean". But the mean assumes a normally distributed set of data, and yours obviously wasn't with an outlier of the 160 data point it was more bi-modal. So, while your story is cute, it really shows how skewed data can affect the result. And, in light of the current "fake news" meme being bandied about, it's an important lesson to objectively question news being presented; the operative term being "objectively".

 

[DrRod]

The better measure of central tendency [the official term] is median -- the point halfway between the range of scores. There is a very small town [22 houses and a campground] near us and the median income for adult males is zero. That means that half the men earn something but half earn nothing.

And remember, you can't close the barn door after the chicken is on fire and expect the preacher to come for supper.

 

[PJ The Kid]

Measure with a micrometer, mark with a crayon, cut with an axe

 

[bob11x]

BTW it is the left side lug nuts on Chryslers products that are left handed. Don't want anyone hurting themselves....

 

[sixdogs]

BTW it is the left side lug nuts on Chryslers products that are left handed. Don't want anyone hurting themselves....

Current models aren't like this are they?

 

[check]

"Average" is a non-statistical term since there are many types of averages. People often use "average" when they really mean "arithmetic mean". But the mean assumes a normally distributed set of data, and yours obviously wasn't with an outlier of the 160 data point it was more bi-modal. So, while your story is cute, it really shows how skewed data can affect the result. And, in light of the current "fake news" meme being bandied about, it's an important lesson to objectively question news being presented; the operative term being "objectively".

There is no assumption of "normality" when you calculate the mean (which is just another word for average). You can have the most warped distribution, and still the mean/average will be calculated exactly the same way: you add up all the numbers and divide by n. It is how you USE the average that matters. Many, many people in everyday life hear the word "average" and automatically think "middle". Bad idea in a lot of cases, especially with a small sample size.

 

[turnkey4099]

BTW it is the left side lug nuts on Chryslers products that are left handed. Don't want anyone hurting themselves....

You sure about that? I was certain it was on the right side but that is many decades ago.