In Exercises 37– 40, without performing any calculations, dete...

Question

In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.

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Accepted Answer

Hi, everyone, let's take a look at this practice problem. Based on the given graph, which measure of central tendency best represents the data? And below the graph we're given a histogram. Where we have our favorite fruit on the X axis, and the frequency on the Y axis. And For our favorite fruits, we have 4 categories. We have apple, banana, orange, and grape. Apple has a frequency of 2 Banana has a frequency of 17. Orange has a frequency of 4, and grape has a frequency of 6. We're also given 4 possible choices as our answers. For choice A, we have mean, for choice B, we have median, for choice C we have mode, and for choice D we have cannot be determined. So, here for this problem, we need to determine which measure of central tendency best describes the data. And so we really have 3 choices to look at. We have the mean, We have the median. And we have the mode. Let's look at each one of these individually. So we call that the mean is the average of all data values. So it is calculated by adding up all the values and then then dividing by the number of values. This is generally useful for numerical data. However, in our case here, we actually have categorical data, since apple, banana, orange, and grape have no numerical values, they're just category labels. So that means that mean is not going to be an appropriate dal tendency to describe this data. Next, we'll look at the median, and recall that the median is the middle value when the data is arranged in order. Like the mean is most appropriate for numerical data, especially when there are outliers. And here again, we don't have numerical data. So that means that it's not going to be appropriate to use the median as the measure of central tendency to represent our data. So finally we're gonna look at mode. So, we call that the mode is the value that occurs most frequently in a data set, and this is especially useful for categorical data. And the type of fruit is an example of the categorical data, which is what we have in this problem. So, from our graph here, we see that banana has the highest frequency, which would make it the mode. So this would make the mode the best measure of central tendency to represent this data. And if we look at our answer choices, this actually corresponds to answer choice D. So, I hope this explanation has been useful, and I'll see you in the next video.

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