Worksheet 03

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Missouri State University, Springfield *

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101

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Statistics

Date

Apr 3, 2024

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pdf

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Uploaded by LieutenantAtomFish41

Juliette Lecomte, Michelle Henderson, Aveen Hasan, Sophia Marcinkiewicz Worksheet 03 1.) Explain why the standard deviation would likely not be a reliable measure of the variability for a distribution of a small amount of data that includes at least one extreme outlier. The standard deviation would likely not be reliable if it includes at least one extreme outlier because it would dominate and completely change the standard deviation. To make it as reliable as we can, we have to take out the outliers or we can’t use a standard deviation because it's too sensitive. The deviation would change completely if the outlier is there/not there, so it is just better to take it out. We can't have one extreme outlier, it would distort the variability if the numbers are too far apart because we subtract the mean in the formula, and the mean would be biased with such deviations. 2.) Explain how a boxplot can be used to determine whether a distribution of values is essentially symmetric. This can be used to determine some type of symmetric as the box part is in the middle and the whiskers lengths and outlier points can give you an idea of the range of data and how far it goes out on both sides. 3.) The standard deviation for a set of 10 observations is 0. What can you determine about the values of the 10 observations. Explain. The smaller the standard deviation is, the less spread out the data set is. The standard deviation for this set of 10 observations is 0, we can then determine that all the observations in the samples are identical, have the same value. 4.) Create a set of sample data with n 5 and x 20 . (Make sure that not all numbers have the same value.) Then calculate the standard deviation for your data set. If you were to add 9 to each number in the data set, what effect would that have on the mean and standard deviation? If you were to multiply each number in the data set by 3, what effect would that have on the mean and standard deviation? If 9 is added to the number of data set then the mean is also increased by 9 and the standard of deviation remains the same. If you multiply each number of data set by 3 then the mean and standard of deviation is also multiplied by 3. n=5 mean=20 The data set is 18,19,20,21,22 S=1.58 If we add 9: 27,28,29,30,31 mean=20 S=1.58 Is we multiply by 3: 54,57,60,63,66 mean=60 S=4.74

5.) Two students take an accounting course from the same professor and had tests on Monday. Shira has class in the morning and Owen has class in the afternoon. Shira’s test score was 74, with her class average at 82 and standard deviation of 8. Owen received a 76 with his class average at 84 with a standard deviation of 6. Assuming that the class test scores follow a symmetric, bell-shaped curve in both classes, which student did better relative to their class? Shira did better because her score lies within 1 standard deviation from her class’s mean. Owen’s score lies within 2 standard deviations from his class’s mean.

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Worksheet 03

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