In Exercises 15 and 16, construct the frequency polygons.

Question

Chicago Commute Times Use the frequency distribution from Exercise 13 in Section 2-1 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?

Accepted Answer

Hello everyone. Let's take a look at this question together. A study was conducted to analyze the commute times in minutes of employees in a metropolitan city. The collected data was grouped into the following frequency distribution, where we have a table containing the commute time in minutes and the frequency for each commute time. Construct a frequency polygon to represent the commute time distribution. Based on the frequency polygon, does the graph suggest that the distribution is skewed? If so, how? So in order to solve this question, we have to recall how to construct a frequency polygon so that we can construct one representing the commute time distribution. And then based on that polygon, does the graph suggest that the distribution is skewed? And if so, how is it skewed? And so the first step in solving. This problem is organizing the given data, which we know that the class midpoints are needed for the frequency polygon, and the class midpoints are calculated as the lower bound plus the upper bound divided by 2. So using the given data of the commute time in minutes and the frequency, we can calculate the class midpoint for each class which are the different commute times in minutes. And as a result, We have the following values of the different class midpoints, and using the data, we then construct our frequency polygon, which to create our frequency polygon, we follow these steps, which includes plotting the class midpoints on the X axis, plotting the frequency values on the Y axis, marking a dot at each midpoint frequency pair, joining the dots using a straight line to form the polygon. And then extending the graph to touch the X-axis before the first and after the last class midpoint. And as a result, we get the following frequency polygon of our class midpoints on the X axis and the frequency on the Y axis. And then we must interpret our frequency polygon, which we know. That the graph shape determines the skewness. So if it is symmetrical, the data is normally distributed. If it has a longer tail on the right, it is positively skewed or right skewed, and if it has a longer tail on the left, it is negatively skewed or left skewed. And looking at our Frequency polygon, we know in this case, the graph shows a slight negative skew because the majority of commute times are higher, but a few lower values extend the distribution to the left, and we know that a longer tail on the left indicates that the shape of the graph is negatively skewed. Therefore, our collected data yields the following frequency polygon, and based on the frequency polygon, the graph shows a slight negative skew. And looking at our answer choices, we can identify that answer choice B is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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In Exercises 15 and 16, construct the frequency polygons.

Chicago Commute Times Use the frequency distribution from Exercise 13 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.Chicago Commute Times Use the frequency distribution from Exercise 13 in Section 2-1 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?