Let's continue with our lab. In this part of the lab, we're going to calculate the revenue and then do some analysis so that we can have some idea about the sensitivity of this revenue estimate. Once we have the customer numbers or we have simulated the number of customers, like we did in the last part of the lab. Calculating the revenue is really easy. So let's just create another column next to the customers. And the revenue is simply going to be number of customers multiplied by the mean value that we calculated. Now just to make sure that this is a persistent number, I'm going to just convert it into absolute reference, F4. And then we can just fill it down till the end. So again, I'm going to use my Shift key and roll down. There we go. So now we have this revenue filled out in the entire column wherever we had the data for the for the number of customers. Now to ease our calculation, what I'm going to do is I'm going to name this name all these cells so that I can easily call this entire array. To do that, we can go to the Excel menu and say insert a name. And I'm going to define a name and call it just revenue. So now I have given this array a name and I can use it for variety of purposes. Now that we have calculated our revenue for all our simulated days, let's go ahead and calculate some statistics for this, specifically mean and standard deviation. So we'll do this for simulated revenue. Let's calculate the mean. I can just call average function for this. And remember, I gave my array a name, revenue, so I'm just going to use that name here so that I don't have to do the entire array. So we get a simulated revenue of 2046.78. Similarly, we can now calculate the standard deviation. And again, I'm going to just name my array here revenue. And that will give me the standard deviation of the simulated revenue. So by doing this now we can calculate both the mean and standard deviation. If we compare it to our mean of the revenue curve that we estimated, 20.50 versus 20.47, pretty close. There is a bit more variability because this is only out of 1000. And then to get to this level of standard deviation, if we simulated many more, then we'll perhaps get to that. But because it's large enough sample, but still a sample. So we'll have slightly higher standard deviation. Besides not having enough replication perhaps the reason here for the variance to be different from what we have estimated in the row 4 above is because we are simply multiplying the randomly generated number of customers with revenue to get the daily revenue therefore we are not accounting for variance that exist inspite of every customer and that perhaps is more of a reason why the variance does not match but for simulation purposes we can try this and if the average spent is quite similar then since the daily revenue estimates are also just estimates based on our assumptions we dont really know which one is true doing both might be actually valuable like subsize Next, let's get some more shape data. And what we are going to do is we're going to get some idea about percentiles. Now what percentiles do that they will tell us for, for a given percentile, let's say 40 percentile, that revenue number will indicate what percentage of revenue values are below that. So this will give us an idea of whole distribution. So let's again just go and fill our array here. So I'm going to do Fill Series and column. I'm going to just keep a difference of 0.05, which represent 5% and the stop value will be 1. So now I have these percentile values. And what I'm going to do is I'm going to get the percentile values from the Excel function percentile. And I'll say in percentile dot inc, which simply means percentile, including that particular percentile. It is asking for an array. We'll give it the name of our revenue array. And then it wants a percentile value, which is 0.05. So this is the value we get. Just fill it down. So now the interpretation of these numbers simply is that they're 15% of the values. Or there's a 15 percent chance that we'll get a revenue of less than 18.39. So that's what it means. So if I look at 0.7, it's saying there is a 70 percent chance that I'll get a revenue of 21.50 or below. Or in other words, chances of getting revenue higher than 21.50 is 30%. Now, again, besides this, we can also keep the persistent data because as you see whenever I type something, these values change, you can hit F9 to get new values. So I am going to just hit it a few times to just show you that these values are going to change. Again. There are lot of random numbers it's drawing, so it takes a little bit of time, but you can simulate it many time and using the technique that we saw in the case of two dice video, We can accumulate the persistent data as well. We can also create a histogram to get a good idea of the distribution, both visually and to get the probability of certain revenues. So for example, how much revenue do we need to get above a certain level and so forth. So for that, we can first create a range, Let's go till 2600 here. So I've created a range from 1700 to 2600. And then what we can do is we can go to our Data tab and choose data analysis. We can choose a histogram. You say, Okay, it's going to be a little slow, but I'm going to specify where our revenue, the array that we named, and then the bin range. I'm going to use a range from 1700, 2600 right here. I'll put the output Starting here And then I want cumulative percentage in the chart output as well. And we'll hit, Okay. Now it will take a little time because every time we change something on the spreadsheet, all the random numbers are drawn, all the calculations are done. So it is a little intense. And depending upon your PC or your machine, it might take up to a couple of minutes before it shows the data. So there we go, we get our histogram. Again. If you remember, this red line shows us the cumulative density. So if we see this, we can see what happens. We can draw a line anywhere and get the corresponding frequency. We'll have to divide by 1000 to get the probability. Or on the right hand side, it does give you that probability. So for the 50 percent probability, you can just sort of draw a line here and get those numbers from that. Or the histogram gives you that number. So I have used 100 as a difference to get better ideas of these probability, you probably should use smaller numbers. So let's say a difference of 25. Then you'll get much more granular understanding of this cumulative density. But it's going to be similar. So for example, 2000 gives us 39 percent. And if we come to here 2000, It's giving us 40%. So it's giving us similar information. You can get It either way. I find percentiles to be more intuitive for me, but for some people, it's more intuitive to use The cumulative density using a histogram. So we'll stop this lab here Next what we're going to do is we're going to look at generating revenues directly. We do have information about the distribution of revenues directly. So we'll try and use that information directly and simulate it. So for example, we'll use the information about daily revenue. We know the mean and standard deviation. This is another way of directly generating this revenue. Now when we do that, there are certain advantages. They're going to be certain disadvantages. And we'll compare the results and see what would be a better way.