STAT 500 Homework 2 Solution (Penn State University)

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Homework 2 (Thirteen problems) Lesson 2 Problem 1 (BY HAND) (5 points): Consider the following three sets of sample observations: Set 1: 8, 9, 10, 11, 12 Set 2: 8, 9, 10, 11, 100 Set... 3: 8, 9, 10, 11, 1000 A) Find the median and IQR for each data set. B) Find the mean and standard deviation for each data set. C) What do these data sets illustrate about the resistance of the median, IQR, mean, and standard deviation? Problem 2 (BY HAND) (5 points): Set 1: 12, 13, 14, 15, 16 A) Find the new mean and standard deviation if four was added to each value in Set 1 of problem 1. B) Find the new mean and standard deviation if four was multiplied to each value in Set 1 of problem 1. C) Discuss the differences between the effect of adding and multiplying a constant had on the mean and standard deviation. 1. (10 points) Using Minitab to make a histogram (Graph > Histogram) of the variable Height. Copy and paste the histogram below. 2. (5 points) How would you describe the shape of the histogram? 3. (5 points) Based on the shape of the histogram, would you expect the mean and median to be somewhat similar or quite different? 4. (10 points) Use Minitab to find the mean and median (Stat > Basic Statistics > Display Descriptive Statistics and do NOT change any of the default statistics selected) of the variable Height. What are the mean and median values and do they agree with what you expected in question 3? 5. (10 points) According to the Empirical Rule (also called the 68-95-99.7 Rule), for bell shaped data we would expect about 68% of all observations to fall within one standard deviation of the mean; about 95% to fall within two standard deviations of the mean; and about all (99.7%) to fall within three standard deviations of the mean. There are a total of 64 height values in the data set. Using the Standard Deviation (refer back to your Minitab output you produced for question 4) apply the Empirical Rule to the Height data by completing the table below 5. (10 points) From question 4, what is the five number summary for the variable Height? 6. (5 points) As this summary relates to the variable Height, what is the interpretation of first and third quartile? 8. (10 points) How well does the Height data comply with these quartiles? That is, of total number of height values how many would we expect to fall at or below these quartiles compared to how many actually fell at or below these quartiles? 9. (5 points) Create the histogram for the variable Exam. Copy and paste the histogram below and describe the shape and relationship between mean and median. 10. (10 points) Now let’s apply the Empirical Rule to a data set that is not symmetrical. For the Exam data the mean is 88 with 11 as the standard deviation. Using this information, complete the following table. 11. (10 points) Outliers and side-by-side boxplots. Outliers are "extreme observations" for a set of data, but how does one determine what is extreme? Boxplots help us in identifying such observations, and side-by-side boxplots are very useful when we want to display quantitative data across levels of a categorical variable, e.g. heights by gender. Create the side-by-side boxplots for Height by Gender. Click Graph > Boxplot > With Groups. Select Heights for the "Graph Variables" and Gender for the "Categorical Variables" and click OK. Copy and paste your graph below and answer the following questions related to the graph. [Show More]

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