Exam 2: Methods for Describing Sets of Data

A study was designed to investigate the effects of two variables - (1)a studentʹs level of mathematical anxiety and (2)teaching method - on a studentʹs achievement in a mathematics Course. Students who had a low level of mathematical anxiety were taught using the traditional Expository method. These students obtained a mean score of 420 with a standard deviation of 20 On a standardized test. Assuming a mound-shaped and symmetric distribution, what percentage Of scores exceeded 380?

The scores for a statistics test are as follows: 73 76 88 77 90 92 98 85 89 89 79 79 50 70 85 61 85 74 18 80 Compute the mean score.

One of the questions posed to a sample of 286 incoming freshmen at a large public university was, ʺDo you have any tattoos?ʺ Their responses are shown below in the pie chart. Please note that the Values shown represent the number of responses in each category. Based on the responses shown in the pie chart, what percentage of the freshmen responded with ʺYes?ʺ

Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 85 and 3, respectively, and the distribution of scores is mound-shaped and symmetric. If a firm wanted to give the best 2.5% of the trainees a big promotion, what test score would be used to identify the trainees in question?

The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score?

Given the sample variance of a distribution, explain how to find the standard deviation.

What characteristic of a Pareto diagram distinguishes it from other bar graphs?

A sample of professional golfers was taken and their driving distance (measured as the average distance as their drive off the tee)and driving accuracy (measured as the percentage of fairways That their drives landed in)were recorded. A scatterplot of the variables is shown below. What relationship do these two variables exhibit?

The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming the distribution of Commuting times is known to be moundshaped and symmetric, what percentage of these Commuting times are between 50 and 110 minutes?

A radio station claims that the amount of advertising each hour has an a mean of 16 minutes and a standard deviation of 1.3 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 13.66 minutes. Based on your observation, what would you infer about the radio stationʹs claim?

At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 98 miles per hour (mph)and the standard deviation of the serve speeds was 9 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. Find the percentage of serves that were hit faster than 80 mph.

An outlier may be caused by accidentally including the height of a six-year-old boy in a set of data representing the heights of 12-year-old boys.

The payroll amounts for all teams in an international hockey league are shown below using a graphical technique from chapter 2 of the text. How many of the hockey team payrolls exceeded $20 million (Note: Assume that no payroll was exactly $20 million)?

The data below show the types of medals won by athletes representing the United States in the Winter Olympics. gold gold silver gold bronze silver silver bronze gold silver silver bronze silver gold gold silver silver bronze bronze gold silver gold gold bronze bronze a. Construct a frequency table for the data. b. Construct a relative frequency table for the data. c. Construct a frequency bar graph for the data.

The data show the total number of medals (gold, silver, and bronze)won by each country winning at least one gold medal in the Winter Olympics. a. Complete the class frequency table for the data. Total Medals Frequency 1-5 6-10 11-15 16-20 21-25 26-30 b. Using the classes from the frequency table, construct a histogram for the data.

Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees To program, and you have been requested to review the performance of one of the trainees on the Final test that was given to all trainees. The mean of the test scores is 75. Additional information Indicated that the median of the test scores was 85. What type of distribution most likely describes The shape of the test scores?

The calculator screens summarize a data set. a. Identify the mean and the median. b. Based only on the mean and the median, do you expect that the data set is skewed to the right, symmetric, or skewed to the left? Explain.

The following data represent the scores of 50 students on a statistics exam. The mean score is 80.02, and the standard deviation is 11.9. 39 51 59 63 66 68 68 69 70 71 71 71 73 74 76 76 76 77 78 79 79 79 79 80 80 82 83 83 83 85 85 86 86 88 88 88 88 89 89 89 90 90 91 91 92 95 96 97 97 98 Find the z-scores for the highest and lowest exam scores.

Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 190 students and recorded how long it took each of them to find a parking spot. The times had a distribution that was skewed to the right. Based on this information, discuss the relationship between the mean and the median for the 190 times collected.

Which measures variability about the mean, the range or the standard deviation?