Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to construct a frequency distribution table with a specified class width. Here's our problem statement: Refer to the accompanying data set and use the 25 home voltage measurements to construct a frequency distribution with five classes. Begin with a lower class limit of 120.8 volts and use a class width of 0.2 volt. Does the result appear to have a normal distribution? Why or why not?
Place the data into StatCrunch
So here we can see the answer fields forming a frequency distribution table. The first value for the lower class limit of the first class is already filled out for us, so “begin with a lower class limit of 120.8 volts” is already done. Now we need to take the data set and compile it into a frequency distribution table in the format that you see here. So to do that, we're going to click on this icon so we can access our data, and then this icon here allows us to upload it into a place of our choice. I'm going to choose StatCrunch.
So here's the data in StatCrunch. Let's move you over here a little bit, size that to get that out of the way. So now that we have our data set, we're done with this window; we can shut it down. So here's our data set.
Find the frequency counts
So we're going to make a frequency distribution in graphical form and then just copy the values from that graphical form over into the tabular form for our answer fields. To do that we're going to go up here in StatCrunch and go to Graph, and I'm going to select Histogram.
First, I need to select the column where my data is located. That's the Home Volts column, so I select that column. Then down here under Type, I'm just gonna leave that at Frequency because we're looking for a frequency distribution; we're just looking for counts, so I leave the type alone. Then I'm gonna put values in here in these two fields — Start at: 120.8 because we were told in the problem statement to start with 120.8 volts. The width: We're told to use a class with 0.2 volts, so I'm going to 0.2 in here.
And then I don't know why whoever was coding StatCrunch didn't make this the default selection because it's extremely useful, but Value above bar — I'm going to check this box next to Value above bar. And you'll see how useful that's going to be in a moment.
All the other default values are fine for our purpose, so we're going to click Compute! Oh, ho, ho, ho, ho, ho, ho! Look at this! Oh, it’s so beautiful. And the best part is Value above bar gives you the values at the tops of each the bars; those are the counts in each of your bins, each of your classes. So guess what we get to do! Oh, we get to just transfer those numbers over! So the first one is 2, the next one is 6, the next one is 10, the next one is 5, and the next one is 2. So there's our frequency counts.
Find the class limits
Now we get to put in our class limits. We start here with 120.8. The class width is 0.2, so the next one is going to be 121.0, or I could just look over here at my graph here in StatCrunch and I'm listed here — these are the lower class limits for each of the bins. So I can just take those numbers and bring them over — 121.2, 121.4, 121.6.
And then the upper class limits. Now here we were instructed — normally when you're constructing a frequency distribution, the upper limit of one bin does not match the lower limit of the next bin. So we need the next number down from 121.0 that's not 120.8, and so that number is going to be for this particular problem halfway in between. So that's going to be 120.9 because 120.9 gets us just to 121.0 but not exactly 121.0.
In other words, I'm taking this last decimal place, and I'm just subtracting 1 from it. I can do the same thing here: 121.2 minus the 0.1 gives me 121.1, or I could have just added 0.2 (the class width) into this upper limit here: 120.9 plus 0.2 gives me 121.1. And I'm just going to continue down with that same pattern to fill in the rest of the table — [121.3], 121.5 and then this one's going to be 121.7. Check my answer. Good job!
So I click Continue to get the rest of the problem. Does the result appear to have a normal distribution? Why or why not? Well, looking back here in my graph in StatCrunch, I can see that the approximate pattern for a normal distribution is for the values to start low, come up to a high point in about the middle of the range, and then come back down to a low value again. That's the pattern that we see here, and so therefore, I'm going to say, “Yes, the frequencies start low, reach a maximum, then become low again, and are roughly symmetric about the maximum frequency.” Notice the word rough. Roughly is exactly what it means — roughly. It's not exact, so here we go. We're gonna select that answer option. Good job!
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