In Exercises 15 and 16, construct the frequency polygons.

Question

Presidents Use the frequency distribution from Exercise 14 in Section 2-1 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?

Accepted Answer

All right, hello everyone. So this question says the table below shows the annual salaries in millions of US dollars of 30 top CEOs grouped into a frequency distribution. Construct a frequency polygon for yourself using the given data and determine whether the distribution is skewed. If so, explain how. So with the Distribution provided, recall that the first step is to determine the midpoint of each class interval. Because when it comes to a frequency polygon. Each class interval is going to be represented as 1 point with 1 X coordinate which is the midpoint, and the Y coordinate which is the frequency of that interval. So the midpoint, if you recall, is equal to the sum of both the upper and lower boundaries of a given class divided by 2. So using this calculation for each of the intervals provided, the midpoints are as follows. For the first, that would be 1.45. For the second it's 2.45. For the third it's 3.45. For the 4th, it's 4.45. For the fifth, it's 5.45. For the 6th, it is 6.95, and for the seventh category, that would be 9.0. So here, we now have the X coordinates that are going to be plotted on the frequency polygon. The Y coordinate, as mentioned before, is the frequency of the corresponding class interval. So here, just to draw an example for visual purposes, once you have all of these points plotted on the graph itself, you would use straight lines to connect them. Which gives you the end result of the completed frequency polygon. And so with the given data set at the frequency polygon should look as follows. So now let's analyze the shape. Now When it comes to determining whether or not. The data is skewed in any direction, the first thing you want to look for is where the maximum happens to be. So here The maximum that is the highest peak of the frequency polygon is at a midpoint of 3.45. So after this peak has been reached, after this maximum, data values begin to steadily decrease. And so because the peak is towards the left side of the graph, the right tail. Which corresponds to those higher frequencies in the frequency distribution, is longer than the left tail, which represents lower salaries. Therefore, because that right tail is longer. The distribution is skewed to the right. So now we've arrived at our final answer, which reads as follows. The distribution is right skewed because the frequencies decrease as the salary increases. And so with that being said, thank you so very much for watching and I hope you found this helpful.

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In Exercises 15 and 16, construct the frequency polygons.
Presidents Use the frequency distribution from Exercise 14 in Section 2-1 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?

Key Concepts

Frequency Distribution

Frequency Polygon

Skewness

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In Exercises 15 and 16, construct the frequency polygons.Presidents Use the frequency distribution from Exercise 14 in Section 2-1 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?