Exam 3: Numerical Descriptive Techniques

Which of the following is a measure of variability?

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.

Generally speaking, if two variables are unrelated, the covariance will be a number close to zero.

Which of the following statements about the median is not true?

The length of the box in a box plot portrays the interquartile range.

The value of the mean times the number of observations equals the sum of the observations.

Pets Survey: A sample of 40 families were asked how many pets they owned. Their responses are summarized in the following table. -Determine the mean, the median, and the mode of the number of pets owned per family.

Which of the following measures of variability is not sensitive to extreme values?

The ____________________ uses both the mean and the standard deviation to interpret standard deviation for bell shaped histograms.

The value for Q₃ can never be smaller than the value for Q₁.

The range is considered the weakest measure of variability.

Q₂ is another name for the ____________________.

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. -Compute the upper quartile.

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. -A.Describe the shape of distribution of donations based on the values of the quartiles. B.Give a possible reason for the shape of this data set, in terms of donations.

Expressed in percentiles, the fifth decile is the 50^th percentile or the median.

There are three statistics used to measure variability in a data set; the range, the ____________________ and the ____________________.

Is the distribution of the number of workers symmetric or skewed? 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. -What does the value of the first quartile tell you?

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

Percentiles can be converted into quintiles and deciles, where quintiles divide the data into fifths and deciles divide the data into tenths.