Exam 3: Numerical Descriptive Techniques

In a perfectly symmetric bell shaped "normal" distribution:

Hours Worked per Week The following data represent the hours worked per week of a sample of 25 employees from a government department: 31, 43, 56, 23, 49, 42, 33, 61, 44, 28, 48, 38, 44, 35, 40, 64, 52, 42, 47, 39, 53, 27, 36, 35, and 20. {Hours Worked per Week Narrative} Compute the sample mean hours.

Yearly Donations The following data represent the yearly donations (in thousands of dollars)of a sample of 13 benefactors: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2. {Yearly Donations Narrative} Compute the lower quartile for the donations.

Which of the following is a property of r , the coefficient of correlation?

Weights of Police Officers The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171. {Weights of Police Officers Narrative} Determine the location and value of the second quartile of the weights.

If a data set is composed of 5 different numbers, there are ____________________ modes.

If the observations are in the millions, a standard deviation of 10 would be considered small. If the observations are all less than 50, a standard deviation of 10 would be considered large.

Which of the following statements is true?

How is the value of the correlation coefficient r affected in each of the following cases? a. Each x value and y is multiplied by 4. b. Each x value is switched with the corresponding y value. c. Each x value is increased by 2.

Salaries of Employees The following data represent the yearly salaries (in thousands of dollars)of a sample of 13 employees of a firm: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2. {Salaries of Employees Narrative} Compare the mean salary with the median salary and use them to describe the shape of the distribution.

Suppose a sample of size 50 has a sample mean of 20. In this case, the sum of all observations in the sample is 1,000.

Hours of Playing Video Games Suppose that the following data provide the hours of playing video games per week for a sample of 15 high school students in Roanoke, Virginia: 5, 11, 25, 19, 18, 20, 27, 13, 8, 10, 15, 19, 18, 9, and 12. {Hours of Playing Video Games Narrative} Determine the location and value of the second quartile.

The mean is a measure of variability.

The following data represent the number of children in a sample of 10 families from a certain community: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2. a. Compute the range. b. Compute the variance. c. Compute the standard deviation. d. Compute the coefficient of variation. e. Explain why in this case range > variance > standard deviation > coefficient of variation.

According to the Empirical Rule, if the data form a bell shaped normal distribution approximately ____________________ percent of the observations will be contained within 3 standard deviations around the mean.

Weights of Police Officers The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171. {Weights of Police Officers Narrative} Determine the location and value of the lower quartile of the weights.

The ____________________ is not as sensitive to extreme values as the ____________________.

Weights of Police Officers The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171. {Weights of Police Officers Narrative} Calculate the 3^rd and 7^th deciles of the data.

Weights of Police Officers The following data represent the weights in pounds of a sample of 25 police officers: 164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171. {Weights of Police Officers Narrative} Construct a frequency distribution for the data, using five class intervals, and the value 130 as the lower limit of the first class.

Suppose your data set contains ages (in years)and you calculate the range, variance, standard deviation, and coefficient of variation for the data. Explain what units each of these measures is in.