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All right, good afternoon.
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We are going to answer question number 44 from your textbook.
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And we were given 50 pieces of data.
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Each piece of data represented the number of hospitals per state.
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So the first thing that you should do is enter your data into your calculator.
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So on our calculator here, you hit stat and then enter.
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You can enter your data into l1.
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It would take your time doing that.
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You have 50 pieces of data.
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Data.
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So you need to take your time, double check your work.
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After you finish entering your data, you should sort it here.
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So i'm going to hit stat.
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I'm going to go down to number two.
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Sort a.
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That means sort ascending.
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And i'm going to hit the blue second button and the number one.
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And you can see l1 appears.
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Hit enter and it's done.
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So if i go back into my list, stat, enter, my data will be ordered from the lowest value to the highest value.
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And that's the first.
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Part.
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So part a says do an expanded frequency distribution.
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So we're going to have this table, and you should have five columns representing class, frequency, midpoint, relative frequency, and cumulative frequency.
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So the class is going to tell us the boundaries of our data.
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So for the first class, i want to know how many pieces of data are between two numbers.
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So that's our class.
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The frequency is i'm going to count how many pieces of data are between these two numbers.
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The midpoint will be the middle of the class.
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The relative frequency, i'm going to figure out the frequency, and then i'm going to divide it by the total, what percentage of data is in that class.
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And then i'll show you how to do the cumulative frequency.
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So the first thing we need to know is the low value and the high value.
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So i could see the low value is seven.
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I could scroll down to the bottom, but instead i'm going to hit stat.
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I'm going to arrow over to calc.
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I'm going to hit enter because i want the first option here, one bar stats.
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I'm going to hit the blue second button and the number one to get l1.
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And if i scroll down a little bit, you can see the five number summary here.
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My minimum is seven and my max is 377.
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So my first class is always going to start with the lowest value.
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So i need to figure out how wide each class is going to be.
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And i need to know how many classes.
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Now, this question prompt specified 8.
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Classes.
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Sometimes if you are on your own, anywhere between five and ten classes would be good.
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So what i need to do to figure out how to find the class width, i need to take the high value, subtract the low value, and divide by eight.
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And that will tell me how wide each class is going to be.
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So if i do that math, i have 370 divided by eight, comes out to be 46 .25.
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You should always round that up to the next whole number.
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That will ensure that you have all.
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All your values account up for in each class.
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And i'll show you what that means in a minute.
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So to get the range of values for our first class, i'm going to take seven and i'm going to add 47.
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So seven plus 47 gives me 54.
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Now, 54 represents the beginning value for the second class.
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So my first class is going to go from 7 to 53.
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And that's 47 values.
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There are 47 values in that.
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And so my first class started with seven.
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I add at 47 to get the beginning of my second class.
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If i add 47 again, that will give me the beginning of my next class, which is 101.
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So that means my second class ends with 100.
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Add 47 again.
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I get 148.
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So that means this guy ends at 147.
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And i keep on doing that.
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And when i get down to this last class, if i take 336 and add 47, that gives me 383.
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So i know my last class should end with 382.
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So your classes should always begin.
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Your first class should begin with the lowest value.
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And then your last class should include the highest value.
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It doesn't have to end with the highest value, but your highest value should be within this.
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Now, the frequency, i'm going to go into my data set, so i'm going to hit stat, enter, and i'm looking for numbers, values between 7 and 53.
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So i'm going to go over to my list here, and i'm going to count how many pieces of data are between 7 and 53.
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Well, 7's my first one, so that's 1, and i'm just going to count down until i reach 53.
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So 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 23.
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So 23.
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There's 23 pieces of data that are within this range.
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And i'm going to do that for all the rest of the classes.
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You'll find that there are 14 pieces of data between 54 and 100.
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And you can see that 100 is included in that data set.
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There are seven pieces of data between 101 and 147.
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There are two pieces of data between 148 and 94.
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There are two pieces of data between 195 and 241.
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But look here, 242 to 288.
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Well, there's no data values in that range.
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There's no data values in 289 to 335, so they're both zero here.
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And then the next one starts at 336 to 382, so that's 2.
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So if you add these down, they should come out to 50.
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We have 50 pieces of data.
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You need to make sure all of them are accounted for.
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To find the midpoint for each class, you just take the class, the values...