To okay for this problem we're giving, given some s east as a a C T scores and going to convert them to s A T scores. And there's a formula for that that were provided to the most important information from a reading. Our problem is that the S A T scores on their scale equals to the A C T scores times 40 plus 151. Break this into two steps. So I'm going to think it had a little bit here and figure out what I want to get the lowest score and the third quarter I'll score and the mean and the median. They all get basically put into that formula. Um, and we'll figure that out using our calculator. So what I want to find is all these scores. And for a second step, I'm gonna do the same thing. But for the standard deviation and for the inter portal range, the i Q. R. A little bit different for a linear transformation. So we call this a linear transformations a little bit different for that. So let's just do first things first. Let's use our calculator over here, and we're gonna take each of the scores that we have, for example, are problems. Statement told us that I think 40 times that 19. That was my lowest score for the easy T. If I take that times 40 and then I add 1 50 970. I like to go in order from lowest to highest. So the mean score is second. So 40 I mean, score. Everything is adjusted by a factor of 40 and everything gets 150 added to it. Same thing for the median. These measures of center and finally for Q three, otherwise known as their quartile brief scored a 30 in it E c T. That translates into this number for the S A. T s levy a scaled score of 13 50. We take a second rate goes down so we know the lowest score for the S a T B clear. Here's the S A T scores What we wanted to find. The Louis translates to a scaled score of 9 10 The mean is a 12 30. The median of the 12 70. Yeah, and the third quartile, which we abbreviate is the Q three often and statistics is 13 50 they all get multiplied and shifted. I have thought about that on the graph. All right. Now, for the next two, I'm gonna go over here and I'm gonna take these two different numbers with standard deviation. Now, for these measures have spread. The standard deviation does not get added by 1 50 Because the standard deviation is just a, um do you think about its a difference between a low on a high between the lower and higher scores? We take the difference so we could add the 1 50 But we subtracted away for both of them. So really, what you need to know is that you just take for standard deviation. You just multiply by 30 and don't have the 1 50 for standard deviation. That's gonna be 400. And for the in a court. Delloreen, same thing. I'm gonna just multiply, Ray, Wait. Let me know will stick going back up. It's most by the 40. The standard deviation were given us three and the Inter quartile Ranger given six again. But both measures have spread, so you don't have the constant number. You just multiply by that multiplying factor. Important effect, you know So for the standard deviation, my end result for the S A. T. The standard deviation would be 120 and minor quartile range is going to be 240. And that's everything we need there. So nice and clearly Books my answers make a little observation in my final as a T scores, measures have spread and all these other scores five number summaries and measures of center.