 Hi, this is Dr. Dines. I'm going to take a few minutes and show you how to solve this histogram problem It's a frequency a relative frequency histogram We need to get here and we need to use it to come up with some percentiles percentages and the problem starts you work in a bank and are asked to recommend the amount of cash to put into a TM each day you don't want to put in too much or too little and Then we need to create the Relative frequency histogram and pick the right one and then we have two questions if you put 8850 in each day What percent of the days would you run out of cash? And then if you are willing to run out of cash for just 10% how much did you put it? So let's show you how you do that using stat crutch again You can click on the icon here get your data and then open in stat crutch So here's the data in stat crutch The first thing we need to do is to get the range of the data and that means we need the men in the max And I do that using stat summary stats columns because our data is in a column select variable one and I'm going to drag down here We need the range selected hold down my control key and windows and then I need the men in the max and I like to store it in a data table just so I can see it click compute so we can see our Range here is 47 The minimum is 59 and the max is 106 Now you could do this using the data Compute expression Instead I find it easier just to use a simple calculator here I've opened up the windows calculator. We're going to take the range of 47 and then divide that By the number of classes which is a equal 5.875 and we always round up to there's integer so that would give us a bin with a class width of six So now we can construct our histogram. We go to graph histogram Our data is in variable one. We select that to make sure it's selected. We want the frequency relative and We want the bin to start at the minimum value, which is 59 and our bin width is 6 now one of the things I want to show you here is we're going to add a Divider for percentages because we want to get the percentages above and below a point and then we click compute So here is our histogram. Let's go to spread it out here a little bit. Okay. The first thing we need to do is to select the right Histogram and in order to make this comparison. I kind of shrunk up I dragged the edges of my histogram and stat crunch so I can make it kind of Squatty and then I look at the patterns and This one the pattern is a little off. It's only got three up and then it scrubs down We've got one two three four up So that helps us get rid of that one now these other three all have a similar pattern So we need to inspect the the axes and look at the bin start and Stop so here on this first one We can see the midpoint of that first bit is 59 and we know that our bin starts at 59 So it's not that one over here This one's got the midpoint of 65 when I hover over my first bin we can see that this upper limit is 65 so that's not the right one and then is 61 point five That looks like the one that it could be 59 to 65. So that is our answer now the next part is if we put in 8850 in the ATM what percent of the day should you? run out of cash and I'm going to Expand this a little bit again so we can see a little better here. Now. Here's that divider that I Had you add and we can just drag that different places and Look at the percentage above and below that point. You can see right here 73 percent below 26.7 above that point and if you Hover over The line there you can see we're at 86.1. So here we got 88 50 and by Inspecting the bins here. I see that this bin goes from 83 in the lower limit in the lower limit The next bin is 95. So 88 50 is going to be in this bin Very close to that. So I'm going to drag this up and see Let's see you can actually that's eighty eight point three 88.5 is 23.3% Which is the answer they want the next part says we want to not run out of cash More than 10% of the time. So how much would we put in there? You're willing to run out I should say no more than 10% of the time So if we drag this divider till we get a total of 10% That's right at 94.9 that's this divider there remember we've got to be in the next bin down So it's got to be less than 95 that's that upper limit And so like say round the air's hundred and that's how they get the 94 10% so I hope this helps