Exam 3: Describing Data Using Numerical Measures

The Empirical Rule states that for a bell-shaped distribution, approximately 95 percent of data should lie within:

A data set in which the mean, median, and mode are all equal is said to be a skewed distribution.

The following data reflect the number of customers who return merchandise for a refund on Monday. Note these data reflect the population of all 10 Mondays for which data are available. Based on these data, what is the standard deviation?

The owner of a local gasoline station has kept track of the number of gallons of regular unleaded sold at his station every day since he purchased the station. This morning, he computed the mean number of gallons. This value would be considered a statistic.

Explain what is meant by percentiles and quartiles.

If a data set has 740 values that have been sorted from low to high, which value in the data set will be the 20th percentile?

At a sawmill in Oregon, a process improvement team measured the diameters for a sample of 1,500 logs. The following summary statistics were computed: Given this information, the boundaries on the box in a box and whisker plot are:

Why is it that when we find the sample standard deviation, we divide by n-1 but when we find the population standard deviation we divide by n?

The Good-Guys Car Dealership has tracked the number of used cars sold at its downtown dealership.Consider the following data as representing the population of cars sold in each of the 8 weeks that the dealership has been open. The population standard deviation is approximately 2.87 cars.

A distribution is said to be symmetric when the sample mean and the population mean are equal.

For ordinal data, ________ is the preferred measure of central location.

You are given the following data: Assuming that the data reflect a sample from a larger population, the sample mean is 30.00.

Data are considered to be right-skewed when the mean lies to the right of the median.

A professor wishes to develop a numerical method for giving grades. He intends to base the grade on homework, two midterms, a project, and a final examination. He wishes the final exam to have the largest influence on the grade. He wants the project to have 10%, each midterm to have 20%, and the homework to have 10% of the influence of the semester grade. For a student with the following grades during the quarter, calculate a weighted average for the course:

It is possible for a set of data to have multiple modes as well as multiple medians, but there can be only one mean.

A set of data is considered to be symmetric if the 3rd quartile is three times larger than the 1st quartile.

Explain when the empirical rule can be used to help describe data in a population or a sample, defining which data distributions cannot be explained by this rule.

Acme Taxi has two taxi cabs. The manager tracks the daily revenue for each cab. Over the past 20 days, Cab A has averaged $76.00 per night with a standard deviation equal to $11.00. Cab B has averaged $200.00 per night with a standard deviation of $18.00. Based on this information, the coefficient of variation for Cab B is 9 percent.

A recent study involving a sample of 3,000 vehicles in California showed the following statistics related to the number of miles driven per day: Q1 = 12, Q2 = 45, and Q3 = 56. Based on these data, if a box and whisker plot is developed, a value of 110 is an outlier.

A marketing manager for the Verizon cell phone company selected a random sample of 250 customers from the list of 10,556 total customers in a particular region. The mean monthly bill for the last six months based on the sample data is $65.70. The manager should realize that the mean bill for all 10,556 customers will actually be much higher than the sample mean of $65.70.