 Statistics and Excel. Normal Distribution Calories Data Example. 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, 1632 Normal Distribution Calories Example tab. We're also uploading transcripts to OneNote so that you can go to the View tab, Immersive Reader Tool, change the language if you so choose being able to then either read or listen to the transcript in multiple different languages, tying into the video presentations with the timestamps. OneNote desktop version here in prior presentations. We've been looking at how we can represent, present, demonstrate different data sets using both mathematical calculations like the mean or average, the quartiles, the median, the mode, as well as with pictorial representations like the box and whiskers, like the histogram. The histogram being the primary tool we typically envision when thinking about the spread of the data and we can use terms to describe the spread of the data on a histogram like it's skewed to the left, the data is skewed to the right. We then thought about lines and curves that can be represented with formulas that can approximate different data sets depending on the circumstances. If we can approximate a data set with a line or curve that has a formula related to it, that would be great because it gives us more predictive power over whatever the data set is representing. We looked at different lines, curves that might have a formula related to it and could represent things in actual nature in real life, including the uniform distribution, binomial distribution, Poisson distribution, exponential distribution, now continuing on with one of the most famous of course of them all, the normal distribution or the bell curve. Remembering, not all data set will conform to any of these distributions. It could be a data set that's too chaotic to conform to a simple line or curve that has an equation for it. However, we have observed in nature that many times things do roughly conform to these patterns and if we can find one that does, then the formula and the curve can be useful. With the bell curve, we've thought about many things in nature like heights and weights and so on often conform to a bell curve type shape. So what we typically want to do is think about what we're looking at. Does the thing we're looking at conform to one of these distributions? We might test out the data to see if that is indeed the case and then we might plot out the curve to give us more predictive power. This time we're going to be looking at calories. Now if you're looking at calorie counts, if we were kind of tracking our calorie counts for example, you would expect that it would follow some kind of normal distribution intuitively because you would think that my calorie count would have to be somewhere pretty steady and not be going too much on the high end or low end at any given time, given the fact that our weight has to be maintaining somewhat constant. So once we have our data, we can sort it and put a table around it which we'll do in Excel. We can sort it by the date or we can sort it by low to high, high to low, this one currently being sorted from high to low. So what's going to be different about this data set than some of the examples that we have had in the past are that because the calories is a pretty small unit of measure then we're going to run into this issue of should we be putting the calorie counts into buckets so that we can better compare our actual calorie count to what we're going to plot when we plot the calorie counts out. So this is going to be a little bit different in that way to what we've seen before with the plotting of the bell curve information for the calories. So our data is on the left. We're going to start with the normal kind of stuff that we do. Does this conform to a bell curve? Well let's do some of our normal calculations. Let's take the mean or average. This would be the formula in Excel to do so. It's at 2189. That would be summing all of the data up and divided by the number of count. Let's take the standard deviation then. This would be the formula for Excel, so that helps us with the spread 815. Let's take the median. That would be the one where we sort all the data. We pick the one in the middle and we're picking the 2062 because this number is fairly close to the mean. The closer it is to the mean, the more likely that it might be conforming to a bell curve. So that's an indication to us the bell curve might be useful. Here's the formula for the median and then the mode. The mode is 10776. Now this one is a little further off than the mean but it's still fairly close. So we're thinking that possibly a bell curve could still be something that would approximate this data set. This would be the mode. Remember that the mode is the one where it's going to have the number appear multiple times and might be more or less useful depending on the type of data that we're looking at. If we're looking at data such as this data which has the unit of measures pretty small, so you might not have the mode where multiple numbers show up that are exactly the same as you would if you had a smaller unit of measure that you were that you were looking at then it would be more likely that the mode would be representing that kind of middle point. Now the next thing we might do is plot this information into a histogram to see if it looks like a bell curve. So here's a histogram of the data just taking this data set putting it into a histogram in Excel. Excel created the buckets from 0 to 730, 730 to 740 calories and so on. The middle point is here which would be some the mean we recall was 2189. So it looks like it's kind of conforming to a bell curve. Remember that the last example that we looked at because we had a whole lot of data points we were looking at heights then the data looked a lot more bell shaped but if you don't have as many data points then it's not going to be as bell shaped but we would still expect that it would look like clumped in the middle and then moving out towards the sides here as the look in shape of something like a histogram which might give us more confidence that this could be conforming to a bell curve scenario so that we can plot a bell curve. So let's plot the bell curve we're going to say all right let's take our x's let's take our p of x's that we will then calculate the question is where should we start with our x's. So the x's we're talking about calories now so you would think you can't have zero calories because they'd have to be just positive calories you cannot have negative calories however in theory remember that the bell curve goes in if indefinitely infinitely on to the left and the right so let's