Problem 1
Make up a dataset of 12 numbers with a positive skew. Use a statistical program to compute the skew. Is the mean larger than the median as it usually is for distributions with a positive skew? What is the value for skew?
Problem 3
Make up three data sets with 5 numbers each that have: (a) the same mean but different standard deviations. (b) the same mean but different medians. (c) the same median but different means.
Problem 4
Find the mean and median for the following three variables: $$ \begin{array}{|c|c|c|} \hline \mathbf{A} & \mathbf{B} & \mathbf{C} \\ \hline 8 & 4 & 6 \\ \hline 5 & 4 & 2 \\ \hline 7 & 6 & 3 \\ \hline 1 & 3 & 4 \\ \hline 3 & 4 & 1 \\ \hline \end{array} $$
Problem 5
A sample of 30 distance scores measured in yards has a mean of \(10,\) a variance of \(9,\) and a standard deviation of 3 (a) You want to convert all your distances from yards to feet, so you multiply each score in the sample by \(3 .\) What are the new mean, variance, and standard deviation? (b) You then decide that you only want to look at the distance past a certain point. Thus, after multiplying the original scores by \(3,\) you decide to subtract 4 feet from each of the scores. Now what are the new mean, variance, and standard deviation?
Problem 6
You recorded the time in seconds it took for 8 participants to solve a puzzle. These times appear below. However, when the data was entered into the statistical program, the score that was supposed to be 22.1 was entered as 21.2 . You had calculated the following measures of central tendency: the mean, the median, and the mean trimmed \(25 \%\). Which of these measures of central tendency will change when you correct the recording error? $$ \begin{array}{|c|} \hline \text { Time (seconds) } \\ \hline 15.2 \\ \hline 18.8 \\ \hline 19.3 \\ \hline 19.7 \\ \hline 20.2 \\ \hline 21.8 \\ \hline 22.1 \\ \hline 29.4 \\ \hline \end{array} $$
Problem 8
You know the minimum, the maximum, and the \(25 \mathrm{th}, 50 \mathrm{th},\) and 75 th percentiles of a distribution. Which of the following measures of central tendency or variability can you determine? mean, median, mode, trimean, geometric mean, range, interquartile range, variance, standard deviation
Problem 10
. Your younger brother comes home one day after taking a science test. He says that some- one at school told him that " \(60 \%\) of the students in the class scored above the median test grade." What is wrong with this statement? What if he had said " \(60 \%\) of the students scored below the mean?"
Problem 11
An experiment compared the ability of three groups of participants to remember briefly- presented chess positions. The data are shown below. The numbers represent the number of pieces correctly remembered from three chess positions. Compare the performance of each group. Consider spread as well as central tendency. $$ \begin{array}{|c|c|c|} \hline \text { Non-players } & \text { Beginners } & \text { Tournament players } \\ \hline 22.1 & 32.5 & 40.1 \\ \hline 22.3 & 37.1 & 45.6 \\ \hline 26.2 & 39.1 & 51.2 \\ \hline 29.6 & 40.5 & 56.4 \\ \hline 31.7 & 45.5 & 58.1 \\ \hline 33.5 & 51.3 & 71.1 \\ \hline 38.9 & 52.6 & 74.9 \\ \hline 39.7 & 55.7 & 75.9 \\ \hline 43.2 & 55.9 & 80.3 \\ \hline 43.2 & 57.7 & 85.3 \\ \hline \end{array} $$
Problem 12
True/False: A bimodal distribution has two modes and two medians.
Problem 13
True/False: The best way to describe a skewed distribution is to report the mean.
