Exam 3: Numerical Descriptive Techniques

The interquartile range is found by taking the difference between the 1st and 3rd quartiles and dividing that value by 2.

The number of hours a college student spent studying during the final exam week was recorded as follows: 7, 6, 4, 9, 8, 5, and 10. Compute s² and s for the data and express the numbers in the appropriate unit.

If the standard deviation of x is 18, the covariance of x and y is 120, the coefficient r = 0.90, then the standard deviation of y is 54.87.

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} Find the modal hours.

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} a. Construct a relative frequency histogram for the data. b. What does the histogram tell you about the distribution of the data?

A sample of 13 college professors has a mean age of 30 years and a standard deviation of 5 years. Suppose that the sample is enlarged to 15 college professors, by including two additional professors that are each 30 years old. Will the standard deviation increase, decrease, or stay the same, and why?

Ages of Retirees A sociologist recently conducted a survey of retirees 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 20 uninsured retirees were as follows: 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 78, 79, 80, 81, 86, 87, 91, 92, 94, and 97. {Ages of Retirees Narrative} Identify the interquartile range of the ages of the uninsured retirees. What does this value tell you about the data?

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} Compare the mean and median hours for these employees and use them to discuss the shape of the distribution.

Q ₂ is another name for the ____________________.

A data sample has a mean of 107, a median of 122, and a mode of 134. The distribution of the data is positively skewed.

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

The middle line inside the box in a box plot represents the ____________________.

In a positively skewed distribution, which of the following is the correct statement?

A box plot is a graphical representation of the 5-number summary.

The ____________________ mean of n returns (or growth rates)is the appropriate mean to calculate if you wish to estimate the mean rate of return (or growth rate)for any single period in the future.

In a bell shaped distribution, there is no difference in the values of the mean, median, and mode.

Which of the following is a measure of variability?

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 upper quartile of the ages.

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

Which of the following summary measures is affected most by extreme values?