Exam 2: Describing Data With Numerical Measures

Ice Cream Cone Sales A neighbourhood ice cream vendor reports the following sales of single-scoop ice cream cones (measured in hundreds of cones) for five randomly selected weeks: 5, 4, 6, 5, and 3. -Refer to the Ice Cream Cone Sales statement. Find the average number of weekly sales of single-scoop ice cream cones.

Amount of Food Sold Suppose the hourly dollar amount of food sold by a local restaurant follows an approximately mound-shaped distribution, with a mean sales level of $400 per hour and a standard deviation of $60 per hour. -Refer to the Amount of Food Sold statement. During a one-hour period, this restaurant had sales at the 84th percentile. What dollar sales figure does this represent?

Solution Volumes An analytical chemist wanted to use electrolysis to determine the number of moles of cupric ions in a given volume of solution. The solution was partitioned into n = 30 portions of 0.2 mL each. Each of the n = 30 portions was tested. The average number of moles of cupric ions for the n = 30 portions was found to be 0.185 mole; the standard deviation was 0.015 mole. -Refer to the Solution Volumes statement. Calculate the intervals ( ), ( ), and ( ).

The mode is the sum of a data set's minimum and maximum values, divided by 2.

Which of the following randomly selected measurements, x, might be considered a potential outlier if it were to be selected from the given population?

Aptitude Tests Twenty-eight applicants interested in working in community services took an examination designed to measure their aptitude for social work. A stem-and-leaf plot of the 28 scores appears below, in which the first column is the count per "branch," the second column is the stem value, and the remaining digits are the leaves. Count Stems Leaves 1 4 6 1 5 9 4 6 3688 6 7 026799 9 8 145667788 7 9 1234788 -Refer to Aptitude Tests table. Does the box plot indicate the presence of any outliers?

In assembling a home appliance, workers generally finish the process within 30 minutes to 1 hour. Occasionally, due to system failures, the assembly process takes a long time, possibly as long as 4 to 5 hours. What is the most appropriate measure of central tendency to use in this case if you want the measure to be representative of most of the observed times? Why is it the most appropriate measure?

A sample of 600 values produced the following summary statistics: and Given this information, which of the following values is the upper fence on a box plot of this data set?

Which of these values represents a lower quartile for the data set 23, 24, 21, and 20?

Job Applicant Test Scores A new manufacturing plant has 20 job openings. To select the best 20 applicants from among the 1000 job seekers, the plant's personnel office administers a written aptitude test to all applicants. The average score on the aptitude test is 150 points, with a standard deviation of 10 points. Assume the distribution of test scores is approximately mound-shaped. -Refer to the Job Applicant Test Scores statement. How many applicants will score between 130 and 160 points?

The median is a measure of centre that divides an ordered array of data into two halves. If the data are arranged in ascending order from smallest to largest, all the observations below the median are smaller than or equal to it, while all the observations above the median are larger than or equal to it.

In a histogram, the proportion of the total area that must be to the left of the median is less than 0.50 if the distribution is skewed to the left.

The following summary statistics were computed from a sample of size 250: and Given this information, which of the following statements is correct?

Aptitude Tests Twenty-eight applicants interested in working in community services took an examination designed to measure their aptitude for social work. A stem-and-leaf plot of the 28 scores appears below, in which the first column is the count per "branch," the second column is the stem value, and the remaining digits are the leaves. Count Stems Leaves 1 4 6 1 5 9 4 6 3688 6 7 026799 9 8 145667788 7 9 1234788 -Refer to Aptitude Tests table. What is the sample mean for this data set?

The distribution of actual volumes of tomato soup in 450 mL cans is thought to be bell-shaped, with a mean of 450 mL and a standard deviation equal to 8 mL. Based on this information, between what two values could we expect 95% of all cans to contain?

Job Applicant Test Scores A new manufacturing plant has 20 job openings. To select the best 20 applicants from among the 1000 job seekers, the plant's personnel office administers a written aptitude test to all applicants. The average score on the aptitude test is 150 points, with a standard deviation of 10 points. Assume the distribution of test scores is approximately mound-shaped. -Refer to the Job Applicant Test Scores statement. One of the applicants scored 192 points on the test. What might you conclude about this test score?

Manufacturing Operation Time In a time study conducted at a manufacturing plant, the length of time to complete a specified operation is measured for each one of n = 40 workers. The mean and standard deviation are found to be 15.2 and 1.40, respectively. -Refer to the Manufacturing Operation Time statement. Describe the sample data using the Empirical Rule.

What percentage of all observations in a data set lie between the 30th percentile and the third quartile?

The following data represent a sample of 10 scores on a 20-point statistics quiz: 16, 16, 16, 16, 16, 18, 18, 20, 20, and 20. After the mean, median, range, and variance were calculated for the scores, it was discovered that one of the scores of 20 should have been an 18. Which of the following pairs of measures will change when the calculations are redone using the correct scores?

If the mean value of a set of data is 83.5 and the median is 72.8, then the third quartile will be at least 83.5.