11 Jul stat assignment
Neatly respond to each prompt. Show all work for full credit. Round to four decimal places.
1. Are the median and mean in any set of data always close together? Give an example to help justify your answer.
2. Can a standard deviation be negative? Why or why not? Explain your answer.
3. A group of 30 introductory statistics students took a 25-item test. The mean and standard deviation were computed; the standard deviation was 0. You know that
a. about half of the scores were above the mean
b. the test was so hard that everyone missed all items
c. a calculation error must have been made in determining the standard deviation
d. everyone correctly answered the same number of items
4. A set of data are put in numerical order, and a statistic is calculated that divides the data set into two equal parts. Which of the following statistics was computed?
a. mean
b. interquartile range
c. standard deviation
d. median
5. Consider the two histograms displayed here. The histogram labeled “Var5” has a mean of 54 and the histogram labeled “Var6” has a mean of 53. Indicate which one has a larger standard deviation and explain how you know that data represented by that histogram has the larger standard deviation.
6. A psychologist is studying the effect of drug and electroshock therapy on a subject’s ability to solve simple tasks. The number of tasks completed in a 10-minute period is recorded for subjects who have been randomly assigned to compare four treatment groups: drug with electroshock, drug without electroshock, no drug with electroshock, and no drug/no electroshock. Sixty-four subjects were randomly selected students from a large local university.
Researchers are interested in comparing the mean number of tasks completed among the four treatment groups.
Results from this study are summarized in the graphic.
a. Match the summary statistics listed above to the correct boxplot.
b. Write a few sentences comparing and contrasting these treatments based on this output and describing the conclusions you can make based on the boxplots.
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