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
OK, let’s try this:
You have to make ten hamburgers out of 1 kilo of meat. Each burger should be 100 grams, right? So you form up your ten burgers, and decide to weigh them to see how close they are to your ideal 100 g burger.
You’re pretty good! 8 of your burgers are 100 g, one is 99, and one is 101. That’s almost perfect. If you put them in a row, they all look exactly the same.
Now, you give another kilo of hamburger to a six year old, and ask him to do the same. He makes 5 really big 191 g patties, and then realizes he’s almost out of meat, so the next four are 10,10,10, and 5 grams. When he puts his in a row, you see 5 enormous patties, and 4 bitty ones, and one itty-bitty one.
Obviously, these are two different ways of making burgers! But in each case, we have ten burgers, and in each case, the average weight is 100g. So they’re the same! But they’re clearly not the same. So how do we *describe* the difference, mathematically, between these two sets of burgers?
That’s what the Standard Deviation (SD) does for us. It tells us how far, on average, a member of a set (one of the burgers) is from the set’s average (our “ideal” burger of 100 g). When the SD is small, as it was in the first case, you will see all the burger weights clustered around the middle (the SD was 0.5). When the SD is large, as in the six-year old’s burgers, the weights will be all over the place (SD was 95).
How do you measure this? Easy – you take the difference from each element (burger) from the middle (the ideal 100 g burger), add the differences together, and divide by the number of elements (burgers). That tells you how far, on average, any burger might be from 100 g.
So, in our first case, we have eight burgers where “burger weight-ideal weight = 0”, one where it’s +1, and one where it’s -1. These add up to … zero! Does that make the SD zero as well?
In fact, in any set, adding up the differences will always add to zero. The differences on the minus side always equal the differences on the positive side. Try a few sets and see. To get over this, mathematicians use a trick of “squaring” each measurement first, (because this way, all the negative numbers get turned into positive ones), adding them all together as positive numbers, and then taking the square root of the total. This lets us add together all the burgers that were too heavy, and all the ones that were too small, and find out what the average difference between any burger and the ideal burger will be.
Latest Answers