Everyone. So in this question, we've been given a set off summary statistics relating to universities on the percentage off freshman who graduate within the expected four years. Is that a first about these questions asking whether we would describe this distribution as symmetric or skewed? And so what we're gonna use is the median on the first and third court tiles to have a look at that as well. Is that me? The first thing we notice is that the mean it's less than the median, so it's already indicating some kind of skew, even though this is looking pretty close. So then we're looking at the 25th percentile, the 75th percentile in the media, and the gap between the 25th percentile on the median here is 10.75 so it's quite a big gap. Where it's got between the median and the third percentile is only 4.85 So you've got a much wider gap between the 25th percentile and the median on the 75 percentile in the media. And so we can see from the combination of those two things that this is left skewed. It's not symmetrical The second part of this question is asking about whether there are any outliers on what we can do to you. What? This out is great. It's offenses. And so we're gonna use the formula that says that that well, in a very concerted school time, minus 1.5 times thank you. Uh, on the third quarter, I'll lost 1.5 times. Like you, uh, these are offenses. Well, that is Do is they tell us whether or not on We expect things to be allies, if they're within events, is then there within the acceptable range. If the outside events is that we would consider him to be unusual and therefore outlines. So for this sort of data, we have key one. All those for, let's say, calculate the school, tell right so 74.75 minus 59 that suggest using the 3rd 1st quarter oil is equal to at 15.6. Now, the ease of using this formula here, I'm just going to click what, 1.5 times like you are is so 1.5 kinds 15.6 is equal to 23.4. So now we've got all the tools to construct defences. If I scroll down a little bit, we have a key one, which is 59 late. Once I minus 23 week for is equal to 35 0.75 But it's a very terrible, uh, defense is gonna use this third call tile five plus 23.4, where this 23 point ball comes from about five times seems sold. Rage. That gives us 98 point. So now we look back, uh, summer statistics over here, and we say, Okay, have we got any violent? Usually within 35.75 When we look at our minimum, we've got 43.2, which is way above 35 on we look at maximum here, you say Okay, if you got anything above 98.15 on the maximum is 87.4, which again is lower than this fence. So we find that we don't have any outliers in this set of data. The third part, this question is asking us to construct a box plot. And this is really easy using this summary data. Another minute, there's no out wires. We can go straight ahead and use this to construct about. So if I just move this down a whistle, we can work from here. So that's draw little space restored. Now, Amax meant that we can see over here is 87. So I'm gonna put 90 at the top here and then down at the bottom because our minimum is only 43. Make this 40 just here so a maximum can go near the top, Appear on our minimum, going to the bottom because I've already got one box. What to build? We don't have Teoh. Be too worried about exact proportions, although it's much easier to see this on squared paper with Rueda, which I would absolutely recommend. So the school tile is at 59 on the third course was 75. That's 74. So it is gonna find were fully where we think 60 would be. So this is going up. 50 said that would be plus 20 by. There's gonna be a little bit under here. So says that that's me just working at my scale slightly and then the 75th quarter 74. So if we're saying that this is civil 65 74 is gonna be about here. There's our books, financial problems goes. And then the median that we found here 69 was much closer to the course. All level. That's good. What's gonna sit just here on this is the box part that we've constructed using this data now. Previously, I made a box plot in sum's stuff rippled You can see here, which just compares a little bit with the one that we've drawn. It's just so you can see a problem one without the sort of rough edges. Um on you can see this is drawn pretty well, and you can definitely see the difference in the height of the median being much closer to the top of this, integral to our range on. That's really indicating that left scheme so it wouldn't ask Teoh. Write a few sentences. And so what you want to talk about is that off the 48 universities that's account here that we were surveyed for this on average, about 68% off the freshmen graduate on time. We know that from this off mean median value here and with the range off the percentages of you of universities goes from about 43% 7% and that's a percentage off graduating freshman. But within those universities on the middle, 50% of universe to universities graduate 59 to 75% or freshman within the four years.