Business analytics data analysis and decision making 5th by wayne l winston chapter 02

May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.Introduction slide 2 of 2  There are four steps in data analysis: 1.. May not b

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DECISION MAKING

Describing the Distribution of a Single Variable

2

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(slide 1 of 2)

 The goal is to present data in a form that

makes sense to people Tools that are used

to do this include:

 Graphs: bar charts, pie charts, histograms,

scatterplots, time series graphs

 Numerical summary measures: counts,

percentages, averages, measures of variability

 Tables of summary measures: totals, averages, counts, grouped by categories

 It is a challenge to summarize data so that the important information stands out clearly.

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Introduction

(slide 2 of 2)

 There are four steps in data analysis:

1 Recognize a problem that needs to be

solved.

2 Gather data to help understand and then

solve the problem.

3 Analyze the data.

4 Act on this analysis.

 It is up to you to ask good questions—

and then take advantage of the most

appropriate tools to answer them.

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Populations and Samples

interest in a study (people, households,

machines, etc.)

 Examples:

 All potential voters in a presidential election

 All subscribers to cable television

 All invoices submitted for Medicare reimbursement

by nursing homes

randomly chosen and preferably

representative of the population as a whole.

 Examples: Gallup, Harris, other polls today

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Data Sets, Variables, and Observations

 A data set is usually a rectangular array

of data, with variables in columns and

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Example 2.1:

Questionnaire Data.xlsx

 Objective: To illustrate variables and observations in a

typical data set.

 Solution: Data set includes observations on 30 people who

responded to a questionnaire on the president’s

environmental policies.

 Variables include: age, gender, state, children, salary, opinion.

 Include a row that lists variable names.

 Include a column that shows an index of the observation.

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Types of Data

(slide 1 of 5)

 A variable is numerical if meaningful

arithmetic can be performed on it

 Otherwise, the variable is categorical

 There is also a third data type , a date

variable.

 Excel ® stores dates as numbers, but dates are treated differently from typical

numbers.

 A categorical variable is ordinal if there

is a natural ordering of its possible

values.

 If there is no natural ordering, it is

nominal

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 It is coded as 1 for all observations in that

category and 0 for all observations not in that

category.

 Categorizing a numerical variable by putting

the data into discrete categories (called bins )

is called binning or discretizing

 A variable that has been categorized in this way is called a binned or discretized variable

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Environmental Data

Using a Different Coding (slide 3 of 5)

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 A continuous variable is the result of an

essentially continuous measurement, such

as weight or height.

 Cross-sectional data are data on a cross section of a population at a distinct point in time.

 Time series data are data collected over time.

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Typical Time Series Data Set

(slide 5 of 5)

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Descriptive Measures for

Categorical Variables

 There are only a few possibilities for

describing a categorical variable, all

based on counting:

 Count the number of categories.

 Give the categories names.

 Count the number of observations in each category (referred to as the count of

 Once you have the counts, you can display

them graphically, usually in a column chart or a pie chart.

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Example 2.2:

Supermarket Transactions.xlsx (slide 1 of 3)

 Objective: To summarize categorical variables in a

large data set.

 Solution: Data set contains transactions made by

supermarket customers over a two-year period.

 Children, Units Sold, and Revenue are numerical

 Purchase Date is a date variable.

 Transaction and Customer ID are used only to identify

 All of the other variables are categorical.

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Example 2.2:

 To get the counts in column S, use Excel’s COUNTIF function.

 To get the percentages in column T, divide each count by the total number of observations.

 When creating charts, be careful to use appropriate scales.

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Example 2.2:

 Another efficient way to find counts for a categorical variable is

to use dummy (0–1) variables.

 Recode each variable so that one category is replaced by 1 and all others by 0.

This can be done using a simple IF formula.

 Find the count of that category by summing the 0s and 1s.

 Find the percentage of that category by averaging the 0s and 1s.

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Descriptive Measures for

Numerical Variables

variables, both with numerical summary

measures and with charts.

distributed, ask:

 What are the most “typical” values?

 How spread out are the values?

 What are the “extreme” values on either end?

 Is the chart of the values symmetric about some middle value, or is it skewed in some direction? Does it have any other peculiar features besides possible skewness?

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Example 2.3:

 Objective: To learn how salaries are distributed across all 2011 MLB

players.

 Solution: Data set contains data on 843 Major League Baseball

players in the 2011 season.

 Variables are player’s name, team, position, and salary.

 Create summary measures of baseball salaries using Excel functions.

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Example 2.3:

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Measures of Central Tendency (slide 1 of 3)

 The mean is the average of all values.

 If the data set represents a sample from some

larger population, this measure is called the

 If the data set represents the entire population, it is called the population mean and is denoted by μ.

 In Excel, the mean can be calculated with the

AVERAGE function.

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 The median is the middle observation when the data are sorted from smallest

to largest.

 If the number of observations is odd, the

median is literally the middle observation.

 If the number of observations is even, the median is usually defined as the average of the two middle observations.

 In Excel, the median can be calculated

with the MEDIAN function.

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 The mode is the value that appears

most often.

 In most cases where a variable is

essentially continuous, the mode is not

very interesting because it is often the

result of a few lucky ties.

 However, it is not always a result of luck

and may reveal interesting information.

 In Excel, the mode can be calculated

with the MODE function.

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Minimum, Maximum,

Percentiles, and Quartiles

 For any percentage p, the pth percentile is the value

such that a percentage p of all values are less than it.

with (approximately) a quarter of all observations.

 The first, second and third quartiles are the percentiles

corresponding to p = 25%, p = 50%,

and p = 75%.

 By definition, the second quartile (p = 50%) is equal to

the median.

calculated with Excel’s MIN and MAX functions, and the percentiles and quartiles with Excel’s PERCENTILE and QUARTILE functions.

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Measures of Variability

(slide 1 of 3)

 The range is the maximum value minus the

minimum value.

 The interquartile range ( IQR ) is the third

quartile minus the first quartile.

 Thus, it is the range of the middle 50% of the data.

 It is less sensitive to extreme values than the

range.

 The variance is essentially the average of the squared deviations from the mean.

 If X i is a typical observation, its squared deviation

from the mean is (X i – mean) 2

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 If at least a few of the observations are far from the

mean, their squared deviations from the mean—and the variance—will be large.

 In Excel, use the VAR function to obtain the sample variance and the VARP function to obtain the

population variance.

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Measures of Variability

(slide 3 of 3)

 A fundamental problem with variance is that it is

in squared units (e.g., $  $ 2 ).

 A more natural measure is the standard

deviation , which is the square root of variance.

the square root of the sample variance.

σ, is the square root of the population variance.

 In Excel, use the STDEV function to find the sample standard deviation or the STDEVP function to find

the population standard deviation.

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Calculating Variance and

Standard Deviation

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Empirical Rules for Interpreting Standard Deviation (slide 1 of 3)

 The interpretation of the standard

deviation can be stated as three

 If the values of a variable are approximately

normally distributed (symmetric and

bell-shaped), then the following rules hold:

 Approximately 68% of the observations are

within one standard deviation of the mean.

 Approximately 95% of the observations are

within two standard deviations of the mean.

 Approximately 99.7% of the observations are

within three standard deviations of the mean.

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Empirical Rules for Baseball Salaries (slide 2 of 3)

 The empirical rules should be applied

with caution, especially when the data are clearly skewed, as illustrated by the calculations for baseball salaries below.

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Empirical Rules for Interpreting Standard Deviation (slide 3 of 3)

 The mean absolute deviation ( MAD ) is the average of the absolute deviations.

calculate MAD.

For many variables, the standard deviation

is approximately 25% larger than MAD.

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Measures of Shape

(slide 1 of 2)

 Skewness occurs when there is a lack

of symmetry.

 A variable can be skewed to the right (or

really large values (e.g., really large

baseball salaries).

 Or it can be skewed to the left (or

really small values (e.g., temperature lows

in Antarctica).

 In Excel, a measure of skewness can be

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Measures of Shape

(slide 2 of 2)

 Kurtosis has to do with the “fatness” of the tails of the distribution relative to the tails of a normal distribution.

 A distribution with high kurtosis has

many more extreme observations.

 In Excel, kurtosis can be calculated with

the KURT function.

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Numerical Summary Measures in the

Status Bar and with StatTools

 If you select multiple cells, summary

measures appear for the selected cells in the status bar at the bottom of the Excel window.

 You can choose the summary measures

that appear by right-clicking the status bar and selecting your favorites.

 Although Excel’s built-in functions can be used to calculate a number of summary measures, a much quicker way is to use the StatTools add-in.

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Example 2.3 (Continued):

Baseball Salaries 2011.xlsx

 Objective: To learn the

fundamentals of StatTools and

use it to generate summary

measures of baseball salaries.

 Solution: First, define a

StatTools data set, by

selecting any cell in the data

set and clicking the Data Set

Manager button

 Then generate summary

measures for the Salary

variable, by selecting

One-Variable Summary from the

Summary Statistics dropdown

list and filling in the dialog box

that appears.

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Charts for Numerical

Variables

 There are many graphical ways to

indicate the distribution of a numerical variable

 For cross-sectional variables:

 Histograms

 Box plots

 For time series variables:

 Time series graphs

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Histograms

 A histogram is the most common type

of chart for showing the distribution of a numerical variable.

 It is based on binning the variable—that is, dividing it up into discrete categories.

 It is a column chart of the counts in the

various categories (with no gaps between the vertical bars).

 A histogram is great for showing the

shape of a distribution—whether the

distribution is symmetric or skewed in

one direction.

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 Objective: To see the shape of the salary

distribution through a histogram.

 Solution: It is possible to create a histogram with

Excel tools only—but it is a tedious process.

 The resulting table of counts is usually called a

frequency table

 The counts are called frequencies

 It is much easier to create a histogram with

StatTools.

 First, designate a StatTools data set.

 Next, select Histogram from the Summary Graphs

dropdown list.

 In the dialog box, select the Salary variable and click OK.

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 Solution: Data set lists the

number of bags that were either

late or lost for 456 flights.

 In the Histogram dialog box,

request 9 bins and set the

minimum and maximum to -0.5

and 8.5.

 StatTools divides the range into

9 equal-length bins.

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Example 2.4:

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