And this question were given 25. 80 c a c t scores of graduating seniors and were asked to make a box plot. So this is part a of the question. So I've already drawn my scale, noting that my lowest number is 14 and my highest number, My high scores 31. So when I looked at the numbers and I arrange them in order from smallest to largest, I saw that there was one score of 14 some in a place an X there for a dot plot. You can use dots or exes, but they all just show up a little bit better, I think in this platform, using an X so ah, one score. 14. No scores of 15 1 score 16 three of 17. So I'll just stack those up, trying to take about the same amount of space for each x one of 18 four at 19 three at 20 three. At 21 no scores a 22 two scores, a 23 one a 24 three a 25 to a 28 and one at 31. So those exes represent each of our 25 different scores. So for Part B were asked to identify in two different ways. Where the number 24 where the data value of 24 um, where it is in terms of depth. In other words, how deep into our data is that looking for the position that so we're look right here. Here's our number 24 and we want to count up in two different ways. So from the lowest and down from the highest. So if we count up one, 2345 6789 10 11 12 13 14 15 16 17 18 We find that it is the 19th number from the lowest number. So the 19 and then if we do the same thing but count down from the highest we see one, 234567 We see that it is the seventh number from the highest, so we can identify it by counting up or by counting down from either of the extremes. Part C asks us to identify the percentile, so we're gonna need to know this formula and times K over 100 is how we can identify what percentile where K is the case percentile and n is the number of numbers. So we know that there are 25 scores. So in this case and equals 25 K is gonna be the little sub script that we have there on P, which stands for percentile. So the first question asks us to identify the fifth percentile. So we have 25 numbers times five, which is K and divide by 100. So we're essentially doing is saying Okay, five over 100 is 5% as a decimal 50.5 I'm multiplying that by 25. So that's going to give us than 5% of 25 which is 1.25 In other words, there 1.25 numbers lower than the fifth percentile. So we're going around that up then to the second position. So if we look on our are set of data here, we see that the second position right there, it's 16. So the pit, the fifth percentile is 16. The next percentile that were asked to identify is the 10th So we'll repeat the same procedure and we see that this is 2.5, which means we are looking for the number that's in the third position. So 123 it's gonna be that number 17 and then were asked to identify the 20th percentile. So again, 25 times 20 over 100. And that turns out to be five. So that means there are five numbers less than that. So we're not looking for the number in the fifth position, but the number that has five numbers less than that. So that means we don't want to go all the way to the sixth number. We want to go halfway between the fifth and the sixth. So we have to identify both the fifth and the sixth number and then take their average. So if we got 123456 my fifth number is 17 and my six number is 18. So I'm gonna take the average of 17 and 18 and intuitively in the middle of that is going to be 17 0.5. So the fifth percentile is 17.5. Okay. For part D were asked to find three more percentiles, but now at the upper end of the percentages, So higher numbers. The 1st 1 that were asked to find is the 99th percentile. The process doesn't change those, so we're still going to use the same formula. So 25 is still end. We're looking for the 99th percentile, and that comes out to be 24.75 So, in other words, were looking for the number in the 25th position. And that makes sense that our largest number would be in the 99th percentile because 99% of the other data values would be lower than that. Now we're asked to find the 90th percentile. Same procedure. That's a nine all nines there, cleaning it up, just a smidge, and that number turns out to be 22.5. So again we'll round up. So we're looking for the number in the 23rd position. So when we're looking for these percent house at the upper end, this 23rd represents references the 23rd number from the lowest. But that's also the third number, down from the highest, which might be easier to identify. So if we kind of count backwards, if that's 25th this will be 24th and this would be then the 23rd number, so that would be 28 and finally were asked to find the 80th percentile. So same procedure. And this turns out to be 20. So again, we've got a number that is Ah, whole number. So that means we're looking for the number that is between the 20th and the 21st. So if we look at that, we'll see. OK, this is 25 24 23 22 2120. These are the 20th and the 21st numbers, and both of them are 25. So halfway between there is gonna be 25.