Exercises 29–34 involve large sets of data, so technology shou...

Question

Exercises 29–34 involve large sets of data, so technology should be used. Complete lists of the data are not listed in Appendix B, but they can be downloaded from the website TriolaStats.com. Use the indicated data and construct the frequency distribution.

Earthquake Depths Use the depths (km) of the 600 earthquakes included in Data Set 24 “Earthquakes.” Use a class width of 10.0 km and begin with a lower class limit of 0.0 km. Does the frequency distribution appear to be a normal distribution?

Accepted Answer

Welcome back, everyone. In this problem, a sports scientists recorded the reaction times in milliseconds of 50 athletes in a reflex test. Construct a frequency distribution using a class width of 50 milliseconds, starting with a lower class limit of 200 milliseconds. Does the frequency distribution suggest a normal distribution? Here we have our table of values. Now remember, what are we trying to figure out here? Our problem tells us that we want to construct the distribution with a class width of 50 milliseconds and a lower class limit of 200 milliseconds. Let's make our table. So we're going to have our class intervals. And we're going to have their frequencies, OK? And now, we just do a a a little table here. And we put our line, right? We know that starting at 200, the class width of 50 gives us 200 to 249, and as we continue, we'll have 250 to 299. 300 to 349. 350 to 399 400 to 449. And then, OK, we're gonna have 450 to 499. And we, this would be our last class because we noticed here that the highest value, if we look back at our data set, the greatest value is 485, OK? So we don't need to go any further with our classes. Now that we have our intervals and frequencies to populate our table, we count how many data points fall into each class range. So for example, for the range 200 to 249, we count all of the values that are within that class that are between those values. If we go to our table from the first row, OK, we can tell that 240 would be in that class. In the 2nd row, OK, if we continue, we go ahead. Seems that there are no values here that would be in the class. Uh, for our 3rd row, we would have 200. 225. From our fourth row, OK, we do some counting here, we'd have 245. 250 is close, but it's not within 200 to 249, so it wouldn't be there, OK. And then in our fifth row, we would have 220 and 230. So how many values do you count? 123456. So the frequency of the interval 200 to 249 is 6. To figure out the frequency for the rest of classes, we just basically do the same thing. So for 250 to 299, you should find that it's 9, 300 to 349 has 10, and I'll leave you to verify that on your own or to count it on your own. 350 to 35 399 is 12, 400 to 449 is 9, and 450 to 499 is 4. So this is our frequency distribution for. Our data set for the reaction times of 50 athletes. No, remember, the second part of our problem statement says we want to figure out if this distribution suggests a normal distribution. How can we tell? We'll recall that this is what a normal distribution looks like, OK? It has a bell pattern and it is symmetric. So if our data values roughly resemble something like this, then we could say that it's an approximate normal distribution. Essentially, if it increases with values, reaches to a peak, and then starts to decrease afterwards. Now if we take our frequencies, OK, let me just draw a makeshift axis here. If we take our frequencies. Then for a first class, we have 6. The second has 9. Well, let me bring the 6 up a bit more. First has 6, the second has 9, the 3rd has 10, the 4th has 12, OK, the 5th has 9, and then the 6th has 4. So if you notice here, even though it's not perfect, we could say that it roughly represents a normal distribution. Thus we can say. That the data. Represents or suggests. An approximate. Nor am I. Distribution. Even though slight deviations may exist, OK, we have some old layers. It's not gonna be perfect. We know that at least it's an approximate normal distribution. It has the symmetry and it follows or it resembles a bell pattern. Thanks for watching everyone. I hope this video helped.

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Key Concepts

Frequency Distribution

Class Width

Normal Distribution

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