use the frequency polygon to identify the class with the great...

Question

use the frequency polygon to identify the class with the greatest, and the class with the least, frequency.

Line graph showing MCAT score frequencies for 90 applicants, peaking at score 512 with highest frequency 15.

Accepted Answer

Welcome back everyone. In this problem, for the provided graph, which class interval has the highest frequency and which class interval has the least frequency? That is not 0. Here we have a frequency polygon of final exam scores plotted against the number of students, and A says the highest frequency is between 70 to 74, while the list is from 58 to 62. B says they are the highest is 74 to 78, and the list is 62 to 66. C says the highest is 74 to 78, and the list is 58 to 62 and 90 to 94. And the DA says the highest is 76 to 80 while the least is 56 to 60. Now in our frequency polygon to find the highest frequency we're basically going to look for the highest point or the peak on the polygon and read its corresponding Y value and X value, that is the number of students and the score's midpoint. Now here, notice that our peak, OK, is at the point where we have 8 students and that is the most students, OK. And if we find our corresponding X file at the midpoint, then that would be at 76. OK. Let me just draw that here. So, let me just make that look a little bit better, striped line. So that would be here at 76. Now, since the class meets points are spaced by 4, as we can tell on our graph, the class width is 4. So for us to figure out what a class is, we'll need to figure out the width of 4, or we need to give a width of 4 here. Let me show it on either side of 76. How can we do that? Well, notice from our graph here that if both of them are between 4 or are spaced by 4, OK, then for the highest point, or for the highest. Frequency OK, given the midpoint. Then that means the lower boundary. It is going to be equal to 76 minus 4 divided by 2 or a half of 4, which is 74. And then the upper boundary. Is going to be equal to 76 plus or divided by 2 or 78. Thus the class intervals. With the highest frequency. Is 74 to 78. And if we look at our graph, that makes sense because if they're spaced by 4 each time, then halfway between 72 and 76 would be 74, and halfway between 76 and 80 would be 78. Know that we have the class interval with the highest frequency. Let's identify one with the least frequency. That is, it's not zero. Where is it on our graph? Well, you probably notice here that the lowest positive Y value is 1, OK? And, and that's above the baseline, that is greater than 0. And that is at the point where our score is 60 and where our score is 92. So, the frequency of one corresponds to two X-axis values. And if we apply the same logic here where we subtract to on either side of our midpoint, OK, then. The class intervals in this case we have 2, so the class intervals with the lowest frequency. OK. Or the lowest frequency, yes, the lowest frequency. Is going to be the class interval that has a midpoint of 60, which is 58 to 62. And the class interval with a midpoint of 92, that is 90 to 94. So the class interval with the highest frequency is 74 to 78, while with the lowest frequency is 58 to 62 and 90 to 94. If we look back at our answer choices, that means that C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

use the frequency polygon to identify the class with the greatest, and the class with the least, frequency.

Key Concepts

Frequency Polygon

Class Frequency

Interpreting Graphs to Identify Extremes

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