Exam 4: Numerical Descriptive Techniques

How do the mean, median, and mode compare to each other when the distribution is: a. symmetric? b. negatively skewed? c. positively skewed?

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.

Ages of Volunteers The following data represent the ages in years of a sample of 25 volunteers from a charitable organization: 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. -{Ages of Volunteers Narrative} Compute the sample variance and sample standard deviation, and express the numbers in the appropriate units.

Test Scores Suppose that an analysis of a set of test scores reveals that: Q₁ = 45, Q₂ = 85, Q₃ = 105. -{Test Scores Narrative} Calculate the interquartile range.What does this tell you about the data?

Statisticians typically apply graphical techniques as a first step in a data analysis because we first need to know the shape of the distribution.

Suppose that a firm's sales were $2,500,000 four years ago, and sales have grown annually by 25%, 15%, -5%, and 10% since that time.What was the geometric mean growth rate in sales over the past four years?

Longevity and Salary A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below: -{Longevity and Salary Narrative} a. Calculate and interpret the covariance between x and y. b. Give a possible reason that the covariance is negative.

Ages of Senior Citizens A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97. -{Ages of Senior Citizens Narrative} Explain why there is no mode for this data set.

The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55.Using Chebysheff's Theorem, 75% of the sales receipts were between $44.65 and $86.85.

Weights of Teachers The following data represent the weights in pounds of a sample of 25 teachers: 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 Teachers Narrative} Compute the sample variance and sample standard deviation.

In a negatively skewed distribution, the distance from the smallest observation to Q₁ exceeds the distance from Q₃ to the largest observation.

Expressed in percentiles, the interquartile range is the difference between the 25th and 75th percentiles.

Three measures of the linear relationship between x and y are the coefficient of correlation, the coefficient of determination, and the coefficient of variation.

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 relative frequency histogram for the data, using five class intervals and the value 130 as the lower limit of the first class.

The number of hours a college student spent studying during the final exam week was recorded as follows: 6, 5, 2, 8, 7, 4, and 9.Compute the range for the data, express the number in the appropriate unit.

In a perfectly symmetric bell shaped "normal" distribution:

Ages of Workers The ages (in years) of three groups of workers are shown below: -{Ages of Workers Narrative} Compute and compare the coefficient of variation for the three samples.

Longevity and Salary A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below: -{Longevity and Salary Narrative} Draw the scatter diagram and plot the least squares line.

The magnitude of the correlation measures the ____________________ of a linear relationship.

Ages of Jockeys The following data represent the ages in years of a sample of 25 jockeys from a local race track: 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. -{Ages of Jockeys Narrative} Find the lower quartile of the ages.