00:01
We have a data set, and we want to transform it to change the mean and standard deviation.
00:06
So when we start out, we have a mean of 12 and a standard deviation of 3.
00:12
We want to get to a mean of 75 and a standard deviation of 12.
00:16
How do we do that? well, the first thing we're going to focus on is the standard deviation, because when we change that, we're going to change the mean as well.
00:25
The standard deviation is a measure of how spread out the data is.
00:30
And we want to make it more spread out.
00:35
So how do we do that? well, we're going to have to multiply every value by something.
00:39
If we look at the formula for a standard deviation, we can see where it's coming from.
00:44
The formula, you take each piece of data, you subtract the mean, you square it, you add up all the squared differences, you divide by the number of pieces of data, and then you square root, because this is the variance, you square root to get the standard deviation.
01:02
So, let's look at the variance.
01:03
Variance, sigma squared.
01:07
Sigma squared is currently nine.
01:10
We want sigma squared to be 12 squared, which is 144.
01:17
How do we get between the two? well, we have 144 divided by 9 is 16.
01:26
What we're going to do is we are going to try to make this difference here larger.
01:35
And how much larger do we need to make it for a difference of times 16, well because it's squared, we need this difference to be four times bigger.
01:46
So we need to multiply this difference here by four.
01:48
And the easiest way to multiply that difference by four is to just multiply every data point by four.
01:55
So this is going to go up.
01:58
All of these are going to go up as well, but it's stretching out the number line.
02:02
If we have the number line going like one, two, three, and four, what we're doing is we're taking it and we are stretching it out...