Hi. So today we're looking at comparing the sugar content off cereals I would be given hissed, aground and sandbox almost close to work with. So the first question is asking us about the range. Now it's really hard to work out the range from history because you have this sort of bucket effects where any values between the low about in the upper bound fall into this book it and so we can't know where the values came from. So every fit, every value in this box could be a zero, and every value could be attending. We would have no way of knowing. And so I'm gonna use my box of despots to estimate the range. So we've got no allies that have been highlighted, and so we can use this top value to estimate the proper value by range. And that's coming in about 60 halfway between these two points. When we look at the lower end, this value here is coming around zero or where I'd expect there to be based on the scale how that no serial realistically has exactly zero sugar content. And so I'm going around that to be one for the sake of realism in this question, and so we expect the range to be 60 minus one. So about 59 is an estimate. The range, based on data that's know perfectly easy to find an accurate range, were the last to describe the shape on. We can use the history wanted. It's really easily as we can see, you've got to clear distinct peaks. And so we've got a by mail distribution going on that follows this sort of double curve thing that's going on. Question three is asking about why this might be. And as we conceive in the boxing with plots, there's two very separate sets of data that are targeted at adults and talk to the Children. And he's a really split on between, you know, down the middle. And so we would expect the the cereals from this peak appears in this sort of mode to be talked to the adults and zeros from this peak to be talked to the Children and similarly, uh, some zeros are targeted, you know, specifically as healthy low sugar cereals, which is bran flakes or fruit and fibre. Where is some cereals are definitely not talking that way, and I talked it because they have lots of sugar and they taste really good. And so you have a really clear distinction between these two camps rather than just we would you know, you wouldn't expect to see the same number of boxes through all these percentages. So part forwards asking us whether all Children cereals are hiring sugar than adults cereals. And so what we can see here is that even the lowest number, the minimum of the Children's target group, is above the maximum value of adults on. So what it tells us is that, yeah, every Children cereal is higher to content than every adult cereal, which is a little bit crazy. But we don't often see that in comparing two data sets so related. Yeah, often as some sort of overlap and questions. I was asking which group of cereals varies more digital content and again, we look at our books on with quotes to wait this out and we can see from the Q R for me in school, tell range. I'm from the general range within each section, a good idea of the spread. So we look at the Children's. There's a quite compact into court, our range going on here on as a fairly short set of whiskers. Whereas for the adults, we have a much wider inter quartile range. Just estimating off this graph. This is gonna be about 10. Whereas this one only looks to be about five. And again we have quite a tall whisker. And so from this fact, and especially from the difference in whipped of the inter quartile range, we would say that the adults cereals very more widely into the content, which again makes sense considering the general pitch off Children cereals that they are for healthy and tasty. Whereas there is quite a wide range of adult cereals all the way from your most healthy zero sugar ones to head, he's a pretty good. Maybe they hope it sugarless don't are gonna be the worst. And so it makes sense that they'd be a bit more than that read when we think about it.