In Exercises 1 and 2, use the data set, which represents the o...

Question

In Exercises 1 and 2, use the data set, which represents the overall average class sizes for 20 national universities. (Adapted from Public University Honors)

37 34 42 44 39 40 41 51 49 31

52 26 31 40 30 27 36 43 48 35

Construct a relative frequency histogram using the frequency distribution in Exercise 1. Then determine which class has the greatest relative frequency and which has the least relative frequency.

Accepted Answer

The following are the ages of 20 participants in a workshop. We have a list of 20 values here. Using 4 classes, construct a relative frequency histogram where you express relative frequencies as percentages. Determine which class interval contains the highest relative frequency. And so, I've started off with a plot of relative frequency on the Y axis, class interval on the X-axis. So, let's go ahead and figure out our values. To find that, we need to set up our class intervals. So, We have 33 as our highest value. And 19 as our lowest value, which will give us 14. Well then take 14. And divide it by the number of preferred classes, we'll say 4 in this case. That gives us 3.5, which we'll just round up to 4. This means then that we'll have 4 classes, starting with 19, we'll go from 19 to 22. 23 to 26. 27 to 30. And 31 to 34. We'll label these on our plot. OK, now let's count how many ages fall into each interval. 19 to 22, we can count, and we notice that there are 5 that fall into this interval. 23 to 26, we'll have 6, 27 to 30, we'll also have 6. And finally, 31 to 34, we'll have 3. Now, for the relative frequency, we'll have to calculate some percentages. We will say 5 divided by our total of 20, multiplied by the percent 100. We can simplify this to get 25%. We'll do the same for every other category. We get 30% for the second one. 30% for the third one. And for our final one. We'll get 15%. Now that we have all of our percentages, we'll plot them on our histogram. We have 25%, so we'll go up to 25%. We didn't have 30%, so go up to 30%. We'll go up to 30 again for the next group. And the final group We will go up to 15. This is our relative frequency histogram. And based on our percentages, we can see that 23 through 26 and 27 through 30. Contain The highest Relative frequency. OK, this is the answer to our problem. I hope to help you solve it. Thank you for watching. Goodbye.

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Key Concepts

Relative Frequency

Histogram

Frequency Distribution

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