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# When the Mode is Better Than the Mean

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1) When is "mode" the better measure?

Think about what you have learned and how you can relate it to your profession, your daily life, or a realistic hypothetical situation.

2) Then, create (invent) a realistic small dataset that can be best described by mode and poorly described by mean.

3) List the dataset.

4) What does the mode tell us about the data?

5) Why is the mean a poor measure for this data?

https://brainmass.com/statistics/descriptive-statistics/mode-better-mean-579930

#### Solution Preview

1. Mode is a better measure than the mean when you have a set of data with one or a few outliers that significantly skews the mean from the rest of the data. An outlier skewing the data will result in a mean that does not convey reliable information about the rest of the dataset. For example, if you are looking at a small company where most of the employees are making a similar amount except for the CEO (who ...

#### Solution Summary

This solution provides an explanation for how the mode can be a better representation of a dataset than the mean. Included is a practical example illustrating a scenario in which the mode is superior.

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## Hypothesis testing using T-test, correlation

1. A teacher wants to describe the results of a particular test. The test grades were 88,78,79,69,83,82,90,94,95,87,85,83,88,89,90,65,76,88,62,90. What would be and how would you find the mean, median, mode, range, variance, standard deviation, an ordered array, a stem-and leaf, a box-and-whiskers and a bar chart of the class scores?

2. A consumer wants to see if a particular Ford model averages more then 20 miles to the gallon. He randomly selects 10 cars of the model to test. Their averages were 22,21,23,18,19,20,21,22,23,22. What test should he do? What were his results? I have to some how measure, the hypothesis, the data, the analysis, and the conclusion in a proper statistical fashion.

3. A consumer wants to test which model car gets better gas mileage, Honda or Toyota. He picked 8 Hondas that average 22,21,23,25,26,28,24,22 for a tank of gas and 8 Toyotas that average 21,19,18,20,21,19,18. Which test do you do to look for a significant difference and what are the results?

4. Eight men take golf lesson. Before the lessons they shoot 104,102,103,107,103,102,101,100 and after the lessons they shoot 98,97,96,95,99,97,96,97 respectively. What test do you do to test for a significant result and what are the results?

5. A consumer wants to test 3 types of cars on mileage at the same time. He adds Nissan to question 3. The averages were 25,226,29,28,27,28,29,30. What test do I perform, and what are the results?

6. If I add eight women to problem 4. They shoot 109,108,109,108,107,106,107,110 in the practice round and 103,102,100,101,98,99,97,96 after the instruction. What test do I do, what would result?

7. Eight people take a math test and score 87,88,89,90,87,86,85,84 and then take an English test and score 74,77,78,79,80,76,75,74 respectively. What test would I use here to test for a relationship, what would be the result?

8. Eight people are ranked on their high school GPA as 1,2,3,4,5,6,7, and 8. They are ranked on their SAT scores as 2,1,4,3,5,6,7, and 8 respectively. What test do I do, what would it result in?

9. Men score 105,102,103,98,99,100,101, and 102 on an I.Q. test. Women score 103,104,105,105,106,110,107, and 106. What test do I do to test for a relationship between the two variables and what would result?

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