Critical Thinking. For Exercises 5–20, watch out for these lit...

Question

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.

Geography Majors The data listed below are estimated incomes (dollars) of students who graduated from the University of North Carolina (UNC) after majoring in geography. The data are based on graduates in the year 1984. The income of basketball superstar Michael Jordan (a 1984 UNC graduate and geography major) is included. Does his income have much of an effect on the measures of center? Based on these data, would the college have been justified by saying that the mean income of a graduate in their geography program is greater than $250,000?

17,466 18,085 17,875 19,339 19,682 19,610 18,259 16,354 2,200,000

Accepted Answer

The following are the estimated annual incomes in dollars of students who graduate from a university with a major in history. The data are based on graduates from a particular year and one exceptionally high income is included. Find the mean median mode and the mid-range to answer the given question. Does the exceptionally high income significantly affect the measures of sinner? Based on these data, would the university be justified in claiming that the mean salary of history graduates exceeds 200,000? We're also given a dataset and 4 possible answers. Now, to solve this, we need to find all of our measures. We have a table here that shows our calculations, but let's see how we can find those. I mean Will be the sum Of all values. Divided by The sample size. Now, if we look at our list of values, we have 16,000. 920 Plus 18,340. And so on Divided by the sample size. In this case, there are 9 observations. This would give us a value of 232,896.67. Now, this is the mean with the outlier. The mean without the outlier means we will take out the last value of 1,950,000. We can see based on the table here that that calculation gives us 18,258.75. We can also look at the median. The median is just the middle of the data set. And if we organize all of these. From the lowest. The highest, we would end up getting 18,340 with our outlier, 18,220 without the outlier. Now, the mode is our most occurring value, but since there's no repeated values, there is no mode, either with or without the outlier. Finally, we can calculate the mid-range. The mid-range is our minimum value. Plus our maximum value. Divided by 2. In this case, we have 16,500. Plus 1,950,000. Divided by 2. This would give us 983,250. Without the outlier We will have Are men plus max divided by 2. Which is 16,500. Plus, our new maximum value. Which ends up being 19,800. Divided by 2, gives us 18,150. We can then see that the mean drops from 230 to 1896 to 18,258. That is a very big drop, which is a large effect. Our median doesn't change very much, and our mode has no effect. But the mid-range does change from 983,000 to 18,000. So the mean and the mid-range dropped drastically. And this shows them, based on just the mean, that the outlier did have a major impact. We can then say that the answer to our problem. I answer the mean and bed ranges are significantly affected by the outlier while the median remains stable. Therefore, saying the university's claim that the mean salary exceeds 200,000 is indeed misleading. OK, I hope that helped me solve the problem. Thank you for watching. Goodbye.

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Key Concepts

Measures of Central Tendency

Outliers

Justification of Claims

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