someone please explain Standard Deviation to me.

Question

First of all, an example; mean age of the children in a test is 12.93, with a standard deviation of .76.

Now, maybe I am just over thinking this, but everything I Google gives me this big convoluted explanation of what standard deviation is without addressing the kiddy pool I’m standing in.

Edit: you guys have been fantastic! This has all helped tremendously, if I could hug you all I would.

In: Mathematics

Answer 1

Let’s say you have a bunch of points on a graph and you find the line of best fit. That line would be floating out amongst the data points with a “distance” between the line and data point. If you take all those distances and average them, you have your standard deviation. It’s the average amount the average deviates from the data.

Let’s say Tom has $1 and Bill has $2. Obviously the average amount of money between Tom and Bill is $1.50, but Tom and Bill deviate from the average by $0.50. Let’s add a third person, Dave, with $6. The average amount of money is $3 between the three guys. Tom deviates by $2 ($3 is the average and Tom has $1; $3-$1=$2), Bill deviates by $1, and Dave deviates by $3. Average those deviations to get a standard deviation of $2. It’s the average distance from the average.