 Statistics and Excel Exponential Distribution create and compare sample line-weighting data to exponential distribution. Got data? Let's get stuck into it with statistics and Excel. You're not required to, but if you have access to OneNote, we're in the icon left-hand side. OneNote Presentation 1580 Exponential Distribution create and compare sample line-weighting data to exponential distribution tab. We're also uploading transcripts to OneNote so that you can go to the View tab, the Immersive Reader tool, change the language if you so choose. Be able to either read or listen to the transcript in multiple different languages, tying in the transcript to the video presentations using the timestamps. OneNote Desktop Version here in prior presentations. We've been thinking about how we can represent different data sets both numerically with calculations like the average or mean, the median, quartiles, and pictorially with things like the box and whiskers and the histogram. The histogram being the primary tool we envision when thinking about the spread of data and we can then describe the data on the histogram using terms such as it's skewed to the left, it's skewed to the right. We're now looking at those families of curves which have functions related to them which often approximate data sets in the real world and if we can approximate a data set with a curve that would be great because it gives us more predictive power with the actual formula. We've been looking at different types of curves in the past that are often represented in real-life scenarios such as the uniform distribution, Poisson distribution, binomial distribution and now we're looking at the exponential distribution remembering that as we saw in a prior presentation it's often related to the Poisson distribution and in practice in a business scenario we often see the Poisson distribution in line waiting situations asking questions such as what's the likelihood of so many people arriving within certain time intervals like one minute or one second and we also could do it over space or distances such as how many potholes are in so many miles of roads or what's the likelihood of so many potholes being in so many miles of road and then if we ask the question for the exponential distribution we kind of flip things on their head asking what's going to be the average interim time between the next arrival for example in a line waiting situation sometimes it's a little bit more difficult to kind of envision the exponential distribution and how it fits into like a line waiting situation so now we're going to do a problem that is going to be similar to what we did in the past for Poisson and binomial meaning we'll try to generate some random numbers that will be equivalent or similar to us actually going out and testing and collecting the data so that we can then compare that actual data to a Poisson distribution which will be the smooth curve so we're going to start off and imagine that the mean arrival time in hours is 10 so we're going to imagine there's 10 arrivals in a line waiting type of situation or a meeting how many people are going to show up in a certain amount of time we're going to say the mean number of arrivals or customers to a restaurant or something like that is going to be 10 note that this is generally the question that we ask when dealing with a Poisson type of distribution which is what's the likelihood that so many people might arrive in some certain time interval in this case an hour the average arrivals we're saying in an hour are going to be 10 in this case now whenever we're dealing with time we always have to ask are we going to be thinking about this in terms of hours and minutes or in seconds in this case let's break it down to the arrivals in minutes so if 10 people are arriving in an hour I can take the 10 divided by 60 I'm going to say about 0.166 people arriving in a minute interval that could be a little bit of an abstract feeling number because now you're saying okay that's obviously less you can't have less than a whole person arriving but obviously it's an average the concept of the average so then we're going to kind of flip this around to go from the Poisson type of question to an exponential question which is the inter arrival time in hours let's first think about it in hours so now we're thinking about how much time on average will be passing between arrivals and so if we have 10 people arriving per hour I can take 1 over 10 and that would give us about 0.1 hours so now we're looking at hours in terms of a fraction of an hour so you know 0.1 hours if we looked at it in terms of minutes I can say okay if there's 0.166 people arriving in a minute so I can then take my calculation and say 1 over 0.166 it goes on forever and then a 7 is about 6 minutes so we have about 6 minutes of the interim time between the arrivals now what we want to do is imagine that we're actually going out there and counting the intervals between arrivals so we're out there at the restaurant or wherever the line is and we're actually counting the time between the arrivals so one person arrives we've got the stopwatch going and then we're going to count