Methods for Describing Sets of Data

Chapter 02 Methods for Describing Sets of Data (text: MacClave, Benson, and Sincich, 9th edition)

Reading: Sections 2.1 through 2.7

Homework: 2.5, 2.10, 2.24 (use histograms), 2.36, 2.42, 2.46, 2.56, 2.62, 2.68, 2.73, 2.76(b only), 2.90, 2.93, 2.140.

Comments:

[1] Much of this stuff you already know: how to calculate averages, medians, etc. The thing to focus on is calculating and understanding how to use the standard deviation. Generally speaking, most managers are experts when dealing with averages, but are less clear on how to use or interpret measures of variation (such as the standard deviation). Variation is everything in statistics. Things vary, people vary, results vary, sales vary, and one has to know how to handle variation.

In business applications of statistics, measuring variation provides a way of measuring uncertainty and uncertainty in business is associated with risk. If you can measure something, you’ve already gone a long way towards understanding and handling it. In this chapter we primarily measure uncertainty by using the sample standard deviation and Section 2.6 gives a glimpse of how we interpret/use this measure. Makes sure you really understand what’s going on in Section 2.6.

[2] Know how to calculate by hand (i.e. calculator) the sample mean, sample variance, and sample standard deviation of a set of data. For the sample variance, make sure you can use either of the two equivalent formulas on page 83 (in box at top of page).

[3] In section 2.2, you can omit the coverage of the so-called Stem-and-Leaf display and just focus on learning how to construct a histogram of a set of data. Most importantly, know how to read the histogram (i.e., use it to find proportions or percentages of the data that lie in various intervals).

[4] Of the two, the Empirical Rule (page 87) is more important than Chebyshev’s theorem (page 87) for applications. I won’t ask questions about Chebyshev’s Rule, so just make sure you know how to use the Empirical Rule.

[5] On exams you should know how to calculate the various measures (means, variances, etc.) by hand (with the help of a calculator) for very small sets of data. Exams are designed to test knowledge of concepts, not lengthy calculations, so data sets on exams are very small. Be sure to use a calculator that can simply calculate the sample standard deviation for you (i.e., you don’t want to waste precious exam time calculating the standard deviation by hand). Excel: All of Excel’s statistics formulas are listed under the fx key at the top of the menu bar in Excel. Just click the fx key and then choose the function category Statistical and the entire list appears on the right side of the menu. For Chapter 02, we only a need a few of these commands/functions, which are listed below:

Make sure you specify a Range of values (such as A1:A25) so Excel knows where to find the data:

Statistic: Excel function (always preceded by an “=” sign)

Sample mean =AVERAGE(A1:A25) Sample median =MEDIAN(A1:A25) Sample variance =VAR(A1:A25) Sample Standard deviation =STDEV(A1:A25) Sample Range =MAX(A1:A25)–MIN(A1:A25)