Tornadoes Listed below are the F-scale intensities of recent t...

Question

Tornadoes Listed below are the F-scale intensities of recent tornadoes in the United States. Construct a frequency distribution. Do the intensities appear to have a normal distribution?

Table displaying frequency counts of tornado F-scale intensities in the United States.

Accepted Answer

All right, hello, everyone. So this question is asking us to construct a frequency distribution for the data given below about the magnitudes of recent earthquakes recorded worldwide. Can we conclude that the magnitudes appear to have a normal distribution? And here we have not only the data set, but also 4 different answer choices labeled A through D. So, before we can determine normality, recall that we first have to construct a frequency distribution, which means that we have to divide this data into class intervals with an appropriate class width. So first, what is the range of the data? Well, examining the data set, we can see that the maximum value, the highest value is 7.3. And the minimum or the lowest value is 4.5. When we subtract the difference between these two valuables, or these two variables, I should say. These two values rather. 7.3, subtracted by 4.5, gives you the range, which in this case is 2.8. And so with this range in mind, we can start off with the minimum value of 4.5, and then use a class width of 0.5. And from there we obtain our intervals. So the first with our minimum would be from 4.5. To 4.9 The next would be 5.0 or 5.0. Up to 5.4. Followed by 5.5 to 5.9. From 6.0 to 6.4. And then from 6.5. To 6.9 And lastly from 7.0 to 7.5. Or 7.4 rather to keep the class width consistent. So that concludes our first column of the table, which are the class intervals. From there, The next portion of the table would be the frequency, that is how many data values of the given set fall into each interval. And so here, the frequency distribution of the given data set is as follows. 8 of the values given fall between the range of 4.5 to 4.9. 6 are between 5.0 to 5.4. 5 are between 5.5 to 5.9. Another 5 are between 6.0 to 6.4. Four are between 6.5 to 6.9. And another four are between 7.0 to 7.4. So now, with this information in mind, does the data fall under a normal distribution? Well, recall that a normal distribution curve should be bell shaped, right, so it should. It should be symmetrical. And the maximum values, the higher values should be towards the middle. So here The frequency should increase to a peak and then decrease symmetrically, with, as mentioned before, the highest frequency in the middle. When you consider the frequency distribution that we made earlier, you can see that the highest frequency. Is actually concentrated towards one side of the data set. That is the highest frequency is actually spread across the lower interval. So therefore, the distribution does not show a clear peak in the symmetrical. And also middle tapering that we discussed earlier. Instead, it actually appears a bit more uniform than it is bell-shaped. So therefore, right, the magnitudes don't follow a normal distribution. Instead, They appear either roughly uniform. With the frequencies of each category being closer together in value. Or you could actually say that they're slightly skewed towards the lower intervals, because the lower interval did have the highest frequency. So going back to the answer choices here, the correct one would be option C in the multiple choice. Which reads that no, the distribution does not appear normal because the frequencies are skewed on one side instead of a single bell-shaped curve. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

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