Hello world,

I had this task to explain to someone who understood maths, but was not a statistician what is "sums of squares". I was free to use graphs to aide him. So I begun. The figure above gives a good approximation of how I explained. I drew a two dimensional plane with observations where the horizontal component was made to depend on the horizontal component. I even used the lines to show that it was actually a summation of the squares of deviation from the expected value.

The other guy apparently could not make out well what the expected value is, and was not comfortable with my using the regression model with a line of best fit to explain it.

A friend was standing nearby. I will soon reply with how he responded since it was not me. A challenge to you upcoming statistician like me, how would you have explained it without using the jargon that someone heard of over 10 years ago while in school?

The response will explain more on my title which is not captured here in this post.

Thanks for following.

### 2 Responses to Standard deviation 101

1. tmawora says:

Hello again,
I mentioned I will comment on the above. Here goes.

My friend never assumed that the other person (client) was familiar with more statistical terms such as Expected value or regression and the like. He went even further down to using just one plane.

He plotted twelve dots, and gave them a fairly equal spread along a number line. Since we have many numbers, he said, we would like one number that would summarize them. He opted for a number with a central weight. This he explained as the mean. Then he noted that the numbers were having different distances from the mean, some negative while others positive. To remove the negative he squared them and summed them to get a single number representative called the sum of squares.
So, it appeared that if he increased the number of measurements, then the sum of squares will increase. In order to have consistency, he divided by the total observations to get what we refer to as a variance.
Then he reasoned, if the measurements were in Kg, the variance would represent summary in square Kg. He therefore got the square root to return to the original scale. He got a deviation, from the mean that was standardized different data-sets called standard deviation.

101 complete.

The next challenge is on simple linear regression. I will explain in detail from a different post.

Good day.

2. maroa sammy maroa says:

clear explanation,thank you!

### Some Maths Links

Vi Hart - Hyperactive videos about beautiful math concepts. Snowdecahedron - A mathematical art installation. Tau - An alternative to pi. BBC Brief History of Math - A Documentary. John Baez - A maths superhero.
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