The analysis of the data has been done using excel statistical sof.docx

The analysis of the data has been done using excel statistical
software. First, the demand and popularity of each product has
been analyzed using pie charts. The extracts from excel shows
the distributions of the three product lines across age, sex and
education. The three types of bicycles have analyzed in terms of
the number of customers using them, sex, and education levels.
The low product line has the highest demand as 80 customers
selected, followed by middle product line with 61 customers and
finally upper product line. The following extracts shows the
demand of the three bicycles on the basis of number of
customers, sex, and education.
Analyzing the popularity and demand for three bicycles using
sex showed that males have a higher proportion of using
bicycles than females. This is show in the following extract and
chart.
Also, the level of education determines the use of bicycles. The
demand for bicycles varies across the different levels of
education. The analysis revealed that non-college high school
diploma do not use bicycles. The following pie chart shows the
proportion of each education level with respect to the use of
bicycles.
Education
Number of Customers
Percentage
Non-High School Diploma
0
0%
High School Diploma

2
1%
Some-College -level work
67
37%
College Degree
97
54%
Graduate Degree at work
14
8%
However, the use of the three products line varied greatly with
the age of customers. The following frequency distribution table
shows the age group of customers and the frequency of using
the three products line.
Bin
Frequency
Cumulative %
Bin
Frequency
Cumulative %
20
10
5.56%
25
62
34.44%
25
62
40.00%
30
45

59.44%
30
45
65.00%
35
32
77.22%
35
32
82.78%
40
16
86.11%
40
16
91.67%
20
10
91.67%
45
8
96.11%
45
8
96.11%
50
7
100.00%
50
7
100.00%
More
0
100.00%
More
0

100.00%
As it can be seen from the histogram, the distribution of age of
customers and the frequency on uses of bikes is negatively
skewed. That is, at early ages, customers use bicycles more than
old ages. At age group 20-25, the demand of bicycles is high
and it decreases as age increases. The mean age, median age,
mode of an average customer is showed in the following table.
The table also shows the average income that most customers
receive,
Mean Age
28.98889
Mode Age
25
Median Age
27
Average Income
35672.22

Median Income
34000
More analysis have been done on individual products lines in
order to determine the mean age of a customer at a given
product line; average salary, average miles/ week, average
times/ week among other analysis. The following discussion
focuses on each of the three product lines.
a) Lower Product Line.
The following analysis shows the profile of an average customer
who chooses to by Low Product Line.
Mean Age
28.6
Sex
Males
55%

Females
45%
Status
Single:
36%
Married.
64%

Mean Salary
30700
Average Miles
88
Average Time/week

3.0125
Mean education Level
3.4625
or ~ 3 (college level Work)
Average Fitness
2.9625
or ~ 3
B) Middle Product Line
Mean Age
29.36066

Average Income:
32967.21
Average Miles/week
83.27869

Average Times/week
2.934426
or ~3
Sex
Males
51%
Females
49%
Marital Status

Single
34%
Married
66%
Average Education Level
3.622951
Average Fitness
2.836066
or 3
c) Upper Product Line

Mean Age
29.36066
Average Income:
32967.21
Average Miles/week
83.27869

Average Times/week
2.934426
or ~3
Sex
Males
51%
Females
49%

Marital Status
Single
34%
Married
66%
Average Education Level
3.622951
Average Fitness
2.836066
or 3

The above analysis shows the profile of a “typical” customer for
each product line.
Why are the numbers for middle and upper product line THE
EXACT SAME?
Compare each of these product-line profiles to the profiles of
typical subscribers of the magazines listed in Table 1.
Recommend the two most appropriate magazine outlets for
advertising each separate product line( Why is there a question
in the middle of the report?)
The age, salary, and number of males (Why did you choose only
3 variables? And why those 3 specifically?will of Table 1 will
(will of Table 1 will?? ) be compared with the values of each
product line. The following table shows a summary profile of
the three product line:
Age
Salary(Income)
% of males
Low Product Line
28.6
30700
55%
Middle
29.4
32967
51%
Upper
29.2
50100
79%
Comparing the above profiles with Table 1, we can locate
magazines that correspond to this date.(data?) The following
magazines should be considered for advertisement.
Age

Salary
% of males
Sporting world
28
31000
52%
Cycle Time
29
60,000
65%
Entrepreneurs’’ Day
26
27,000
90%
Outdoor Fun
27
30,000
55%
Software Review
28
48,000
60%
Who is Hot in Sports
25
22,000
80%
Low Product Line has the highest demand, followed by Middle
Product Line, and then Upper Product Line. To ensure that each
product is well advertised the following final list of magazines
should be implemented.
· Sporting world
· Software Review
· Entrepreneurs’’ Day
· Outdoor Fun
· Cycle Time.

Question: Why did we take out “Who is Hot in Sports”?
Because of budget or what?
The above list has been chosen on the basis of age and
percentage of males. Those magazines with low percentage of
males should be ignored since they will lead to low performance
of advertising strategy. More so, those magazines whose
subscribers are above 30 should be the last in the priority list.
Five different( how did you come up with five?) magazine
outlets should established to ensure that every product line is
advertised at least twice. The bicycles with low demand should
be advertised more while those with relatively less.
The cost in advertisement is $2000 per half page in the chosen
magazines. If the advertisement is made 5 times in each issue
for four years, then the cost of advertising will be given;
Cost per page * Number of Outlets* Number of Run times *
Number of years.
Therefore, the total cost of advertising will be;
2000*5*5*4 = 200,000 (I understand that this is right because it
is under budget but how did you decide that only 5 outlets are
needed instead of 6?
This figure represent 83.333% percent of the total Budget. The
percentage is calculated as follows;
(200,000/240,000)*100 = 83.333%
However, this values assumes no risk associated with choosing
bad magazines. The company has set $240,000 dollars for
advertisement. However, the value should be flexible and have a
range of $200,000 to $300,000 to allow for changes in market.
What do you mean? Because if they exceed 240,000 than they
will be over budget.
Histogram
Frequency 20 25 30 35 40 45 50 More 10
62 45 32 16 8 7 0 Cumulative % 20 25
30 35 40 45 50 More 5.555555555555549E-
2 0.4 0.65000000000000024 0.82777777777777817
0.91666666666666596 0.96111111111111103 1 1

Bin
Frequency
Product Line Demand
Percentage demand
Lower Product Line Middle Product LineUpper Product Line
0.44444444444444414 0.33888888888888935
0.21666666666666701
Sex Distribution
Male Female 106 74
Number of Customers Non-High School Diploma High
School Diploma Some-College -level work College
Degree Graduate Degree at work 0 2 67 97 14
Percentage Non-High School Diploma High School
Diploma Some-College -level work College Degree
Graduate Degree at work 0 1.1111111111111101E-2
0.37222222222222212 0.53888888888888919
7.7777777777777821E-2
Products LineNumber of CustomersPercentage demand
Lower Product Line8044%
Middle Product Line6134%
Upper Product Line3922%
SexNumber
Male106
Female74

Chap 3-1
Chapter 3
Numerical Descriptive Measures
Statistics for Managers Using Microsoft Excel
7th Edition
Statistics for Managers Using Microsoft Excel® 7e Copyright
©2014 Pearson Education, Inc.
Chap 3-2
In this chapter, you learn:
To describe the properties of central tendency, variation, and
shape in numerical data
To compute descriptive summary measures for a population
To construct and interpret a boxplot
To calculate the covariance and the coefficient of correlation
Learning Objectives

Chap 3-3
Summary Definitions
The central tendency is the extent to which all the data values
group around a typical or central value.
The variation is the amount of dispersion or scattering of values
The shape is the pattern of the distribution of values from the
lowest value to the highest value.
DCOVA
Chap 3-4
Measures of Central Tendency:

The Mean
The arithmetic mean (often just called the “mean”) is the most
common measure of central tendency
For a sample of size n:
Sample size
Observed values
The ith value
Pronounced x-bar
DCOVA
Chap 3-5
The Mean
The most common measure of central tendency
Mean = sum of values divided by the number of values
Affected by extreme values (outliers)
(continued)

11 12 13 14 15 16 17 18 19 20
Mean = 13
11 12 13 14 15 16 17 18 19 20
Mean = 14
DCOVA
Chap 3-6
The Median

In an ordered array, the median is the “middle” number (50%
above, 50% below)
Not affected by extreme values
Median = 13
Median = 13
11 12 13 14 15 16 17 18 19 20
11 12 13 14 15 16 17 18 19 20
DCOVA

Chap 3-7
Locating the Median
The location of the median when the values are in numerical
order (smallest to largest):
If the number of values is odd, the median is the middle number
If the number of values is even, the median is the average of the
two middle numbers
Note that is not the value of the median, only the
position of
the median in the ranked data
DCOVA

Chap 3-8
The Mode
Value that occurs most often
Not affected by extreme values
Used for either numerical or categorical (nominal) data
There may may be no mode
There may be several modes
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Mode = 9
0 1 2 3 4 5 6

No Mode
DCOVA
Chap 3-9
Review Example
House Prices:
$2,000,000
$ 500,000
$ 300,000
$ 100,000
$ 100,000
Sum $ 3,000,000
Mean: ($3,000,000/5)
= $600,000
Median: middle value of ranked data
= $300,000
Mode: most frequent value
= $100,000
DCOVA

Chap 3-10
Which Measure to Choose?
The mean is generally used, unless extreme values (outliers)
exist.
The median is often used, since the median is not sensitive to
extreme values. For example, median home prices may be
reported for a region; it is less sensitive to outliers.
In some situations it makes sense to report both the mean and
the median.
DCOVA
Chap 3-11
Measure of Central Tendency For The Rate Of Change Of A
Variable Over Time:
The Geometric Mean & The Geometric Rate of Return

Geometric mean
Used to measure the rate of change of a variable over time
Geometric mean rate of return
Measures the status of an investment over time
Where Ri is the rate of return in time period i
DCOVA
Chap 3-12
The Geometric Mean Rate of Return: Example
An investment of $100,000 declined to $50,000 at the end of
year one and rebounded to $100,000 at end of year two:
The overall two-year return is zero, since it started and ended at
the same level.
50% decrease 100% increase
DCOVA

Chap 3-13
The Geometric Mean Rate of Return: Example
Use the 1-year returns to compute the arithmetic mean and the
geometric mean:
Arithmetic mean rate of return:
Geometric mean rate of return:
Misleading result
More
representative
result
(continued)
DCOVA

Chap 3-14
Summary
Central Tendency
Arithmetic Mean
Median
Mode
Geometric Mean

Middle value in the ordered array
Most frequently observed value
Rate of change of
a variable over time
DCOVA
Chap 3-15
Same center,
different variation
Measures of Variation
Measures of variation give information on the spread or
variability or dispersion of the data values.
Variation
Standard Deviation
Coefficient of Variation

Range
Variance
DCOVA
Chap 3-16
Measures of Variation:
The Range
Simplest measure of variation
Difference between the largest and the smallest values:
Range = Xlargest – Xsmallest

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Range = 13 - 1 = 12
Example:
DCOVA
Chap 3-17
Why The Range Can Be Misleading
Ignores the way in which data are distributed
Sensitive to outliers

7 8 9 10 11 12
Range = 12 - 7 = 5
7 8 9 10 11 12
Range = 12 - 7 = 5
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120
Range = 5 - 1 = 4
Range = 120 - 1 = 119
DCOVA
Chap 3-18

Average (approximately) of squared deviations of values from
the mean
Sample variance:
The Sample Variance
Where
= arithmetic mean
n = sample size
Xi = ith value of the variable X
DCOVA
Chap 3-19
The Sample Standard Deviation
Most commonly used measure of variation
Shows variation about the mean
Is the square root of the variance
Has the same units as the original data
Sample standard deviation:

DCOVA
Chap 3-20
The Standard Deviation
Steps for Computing Standard Deviation
1. Compute the difference between each value and the mean.
2. Square each difference.
3. Add the squared differences.
4. Divide this total by n-1 to get the sample variance.
5. Take the square root of the sample variance to get the
sample standard deviation.
DCOVA

Chap 3-21
Sample Standard Deviation:
Calculation Example
Sample
Data (Xi) : 10 12 14 15 17 18 18 24
n = 8 Mean = X = 16
A measure of the “average” scatter around the mean
DCOVA
Chap 3-22
Comparing Standard Deviations
Mean = 15.5
S = 3.338

11 12 13 14 15 16 17 18 19 20 21
11 12 13 14 15 16 17 18 19 20 21
Data B
Data A
Mean = 15.5
S = 0.926
11 12 13 14 15 16 17 18 19 20 21
Mean = 15.5
S = 4.567
Data C

DCOVA
Chap 3-23
Comparing Standard Deviations
Smaller standard deviation
Larger standard deviation
DCOVA
Chap 3-24

Summary Characteristics
The more the data are spread out, the greater the range,
variance, and standard deviation.
The more the data are concentrated, the smaller the range,
If the values are all the same (no variation), all these measures
will be zero.
None of these measures are ever negative.
DCOVA
Chap 3-25
The Coefficient of Variation
Measures relative variation
Always in percentage (%)
Shows variation relative to mean
Can be used to compare the variability of two or more sets of
data measured in different units
DCOVA

Chap 3-26
Comparing Coefficients of Variation
Stock A:
Average price last year = $50
Standard deviation = $5
Stock B:
Both stocks have the same standard deviation, but stock B is
less variable relative to its price
DCOVA

Chap 3-27
Comparing Coefficients of Variation
Stock A:
Stock C:
Stock C has a much smaller standard deviation but a much
higher coefficient of variation
DCOVA
(continued)

Chap 3-28
Locating Extreme Outliers:
Z-Score
To compute the Z-score of a data value, subtract the mean and
divide by the standard deviation.
The Z-score is the number of standard deviations a data value is
from the mean.
A data value is considered an extreme outlier if its Z-score is
less than -3.0 or greater than +3.0.
The larger the absolute value of the Z-score, the farther the data
value is from the mean.
DCOVA
Chap 3-29
Z-Score
where X represents the data value
X is the sample mean
S is the sample standard deviation

DCOVA
Chap 3-30
Z-Score
Suppose the mean math SAT score is 490, with a standard
deviation of 100.
Compute the Z-score for a test score of 620.
A score of 620 is 1.3 standard deviations above the mean and
would not be considered an outlier.
DCOVA

Chap 3-31
Shape of a Distribution
Describes how data are distributed
Two useful shape related statistics are:
Skewness
Measures the extent to which data values are not symmetrical
Kurtosis
Kurtosis affects the peakedness of the curve of the
distribution—that is, how sharply the curve rises approaching
the center of the distribution
DCOVA
Chap 3-32
Shape of a Distribution (Skewness)
Measures the extent to which data is not symmetrical

Mean = Median
Mean < Median
Median < Mean
Right-Skewed
Left-Skewed
Symmetric
DCOVA
Skewness
Statistic
< 0 0 >0

Chap 3-33
Shape of a Distribution -- Kurtosis measures how sharply the
curve rises approaching the center of the distribution)
Sharper Peak
Than Bell-Shaped
(Kurtosis > 0)
Flatter Than
Bell-Shaped
(Kurtosis < 0)
Bell-Shaped
(Kurtosis = 0)
DCOVA
Chap 3-34
General Descriptive Stats Using Microsoft Excel Functions
DCOVA

Chap 3-35
General Descriptive Stats Using Microsoft Excel Data Analysis
Tool
Select Data.
Select Data Analysis.
Select Descriptive Statistics and click OK.
DCOVA
Chap 3-36
General Descriptive Stats Using Microsoft Excel

4. Enter the cell range.
5. Check the Summary Statistics box.
6. Click OK
DCOVA
Excel output
Microsoft Excel
descriptive statistics output,
using the house price data:
House Prices:
$2,000,000
500,000
300,000
100,000
100,000
DCOVA
Chap 3-37

Chapter 3 3-‹#›
Basic Business Statistics, 10/e © 2006 Prentice Hall, Inc.
Chap 3-38
Quartile Measures

Quartiles split the ranked data into 4 segments with an equal
number of values per segment
25%
The first quartile, Q1, is the value for which 25% of the
observations are smaller and 75% are larger
Q2 is the same as the median (50% of the observations are
smaller and 50% are larger)
Only 25% of the observations are greater than the third quartile
Q1
Q2
Q3
25%
25%
25%
DCOVA
Chap 3-39

Quartile Measures:
Locating Quartiles
Find a quartile by determining the value in the appropriate
position in the ranked data, where
First quartile position: Q1 = (n+1)/4 ranked value
Second quartile position: Q2 = (n+1)/2 ranked value
Third quartile position: Q3 = 3(n+1)/4 ranked value
where n is the number of observed values
DCOVA
Chap 3-40
Quartile Measures:
Calculation Rules
When calculating the ranked position use the following rules
If the result is a whole number then it is the ranked position to
use
If the result is a fractional half (e.g. 2.5, 7.5, 8.5, etc.) then
average the two corresponding data values.

If the result is not a whole number or a fractional half then
round the result to the nearest integer to find the ranked
position.
DCOVA
Chap 3-41
(n = 9)
Q1 is in the (9+1)/4 = 2.5 position of the ranked data
so use the value half way between the 2nd and 3rd values,
so Q1 = 12.5
Quartile Measures:
Locating Quartiles
Sample Data in Ordered Array: 11 12 13 16 16 17 18
21 22
Q1 and Q3 are measures of non-central location
Q2 = median, is a measure of central tendency
DCOVA

Chap 3-42
(n = 9)
Q1 is in the (9+1)/4 = 2.5 position of the ranked data,
so Q1 = (12+13)/2 = 12.5
Q2 is in the (9+1)/2 = 5th position of the ranked data,
so Q2 = median = 16
Q3 is in the 3(9+1)/4 = 7.5 position of the ranked data,
so Q3 = (18+21)/2 = 19.5
Quartile Measures
Calculating The Quartiles: Example
Sample Data in Ordered Array: 11 12 13 16 16 17 18
21 22
Q1 and Q3 are measures of non-central location
Q2 = median, is a measure of central tendency
DCOVA

Chap 3-43
Quartile Measures:
The Interquartile Range (IQR)
The IQR is Q3 – Q1 and measures the spread in the middle 50%
of the data
The IQR is also called the midspread because it covers the
middle 50% of the data
The IQR is a measure of variability that is not influenced by
outliers or extreme values
Measures like Q1, Q3, and IQR that are not influenced by
outliers are called resistant measures
DCOVA
Chap 3-44
Calculating The Interquartile Range
Median
(Q2)

X
maximum
X
minimum
Q1
Q3
Example:
25% 25% 25% 25%
12 30 45 57 70
Interquartile range
= 57 – 30 = 27
DCOVA
Chap 3-45
The Five Number Summary
The five numbers that help describe the center, spread and
shape of data are:
Xsmallest

First Quartile (Q1)
Median (Q2)
Third Quartile (Q3)
Xlargest
DCOVA
Chap 3-46
Relationships among the five-number summary and distribution
shapeLeft-SkewedSymmetricRight-SkewedMedian – Xsmallest
>
Xlargest – MedianMedian – Xsmallest
≈
Xlargest – MedianMedian – Xsmallest
<
Xlargest – MedianQ1 – Xsmallest
>

Xlargest – Q3Q1 – Xsmallest
≈
Xlargest – Q3Q1 – Xsmallest
<
Xlargest – Q3Median – Q1
>
Q3 – MedianMedian – Q1
≈
Q3 – MedianMedian – Q1
<
Q3 – Median
DCOVA
Five Number Summary and

The Boxplot
The Boxplot: A Graphical display of the data based on the five-
number summary:
Chap 3-47
Example:
Xsmallest -- Q1 -- Median -- Q3 -- Xlargest
25% of data 25% 25% 25% of data
of data of data
Xsmallest Q1 Median Q3 Xlargest
DCOVA
Chap 3-48
Five Number Summary:
Shape of Boxplots
If data are symmetric around the median then the box and
central line are centered between the endpoints
A Boxplot can be shown in either a vertical or horizontal

orientation
Xsmallest Q1 Median Q3 Xlargest
DCOVA
Chap 3-49
Distribution Shape and
The Boxplot
Right-Skewed
Left-Skewed
Symmetric

Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
DCOVA

Chap 3-50
Boxplot Example
Below is a Boxplot for the following data:
0 2 2 2 3 3 4 5 5 9 27
The data are right skewed, as the plot depicts
0 2 3 5 27
Xsmallest Q1 Q2 / Median Q3 Xlargest
DCOVA

Chap 3-51
Numerical Descriptive Measures for a Population
Descriptive statistics discussed previously described a sample,
not the population.
Summary measures describing a population, called parameters,
are denoted with Greek letters.
Important population parameters are the population mean,
DCOVA
Chap 3-52
Numerical Descriptive Measures
for a Population: The mean µ
The population mean is the sum of the values in the population
divided by the population size, N

μ = population mean
N = population size
Where
DCOVA
Chap 3-53
Average of squared deviations of values from the mean
Population variance:
Numerical Descriptive Measures For A Population: The
Variance σ2
Where
μ = population mean
N = population size
DCOVA

Chap 3-54
Numerical Descriptive Measures For A Population: The
Standard Deviation σ
Most commonly used measure of variation
Shows variation about the mean
Is the square root of the population variance
Has the same units as the original data
Population standard deviation:
DCOVA
Chap 3-55
Sample statistics versus population
parametersMeasurePopulation ParameterSample
StatisticMeanVarianceStandard Deviation

DCOVA
Chap 3-56
The empirical rule approximates the variation of data in a bell-
shaped distribution
Approximately 68% of the data in a bell shaped distribution is
within 1 standard deviation of the mean or
The Empirical Rule

68%
DCOVA
Chap 3-57
Approximately 95% of the data in a bell-shaped distribution lies
within two standard deviations of the mean, or µ ± 2σ
Approximately 99.7% of the data in a bell-shaped distribution
lies within three standard deviations of the mean, or µ ± 3σ
The Empirical Rule

99.7%
95%
DCOVA
Chap 3-58
Using the Empirical Rule
Suppose that the variable Math SAT scores is bell-shaped with a
mean of 500 and a standard deviation of 90. Then,

68% of all test takers scored between 410 and 590 (500 ±
90).
95% of all test takers scored between 320 and 680 (500 ±
180).
99.7% of all test takers scored between 230 and 770 (500 ±
270).
DCOVA
Chap 3-59
Regardless of how the data are distributed, at least (1 - 1/k2) x
100% of the values will fall within k standard deviations of the
mean (for k > 1)
Examples:
(1 - 1/22) x 100% = 75% ….............. k=2 (μ ± 2σ)
(1 - 1/32) x 100% = 88.89% ……….. k=3 (μ ± 3σ)
Chebyshev Rule
Within
At least
DCOVA

We Discuss Two Measures Of The Relationship Between Two
Numerical Variables
Scatter plots allow you to visually examine the relationship
between two numerical variables and now we will discuss two
quantitative measures of such relationships.
The Covariance
The Coefficient of Correlation
Chap 3-60
Chap 3-61
The Covariance
The covariance measures the strength of the linear relationship

between two numerical variables (X & Y)
The sample covariance:
Only concerned with the strength of the relationship
No causal effect is implied
DCOVA
Chap 3-62
Covariance between two variables:
cov(X,Y) > 0 X and Y tend to move in the same direction
cov(X,Y) < 0 X and Y tend to move in opposite directions
cov(X,Y) = 0 X and Y are independent
The covariance has a major flaw:
It is not possible to determine the relative strength of the
relationship from the size of the covariance
Interpreting Covariance

DCOVA
Chap 3-63
Coefficient of Correlation
Measures the relative strength of the linear relationship between
two numerical variables
Sample coefficient of correlation:
where
DCOVA

Chap 3-64
Features of the
Coefficient of Correlation
The population coefficient of correlation is referred as ρ.
The sample coefficient of correlation is referred to as r.
Either ρ or r have the following features:
Unit free
Ranges between –1 and 1
The closer to –1, the stronger the negative linear relationship
The closer to 1, the stronger the positive linear relationship
The closer to 0, the weaker the linear relationship
DCOVA
Chap 3-65
Scatter Plots of Sample Data with Various Coefficients of
Correlation

Y
X
Y
X
r = -1
r = -.6
r = +.3
r = +1

Y
X
r = 0
DCOVA
Chap 3-66
The Coefficient of Correlation Using Microsoft Excel Function
DCOVA

Chap 3-67
The Coefficient of Correlation Using Microsoft Excel Data
Analysis Tool
Select Data
Choose Data Analysis
Choose Correlation & Click OK
DCOVA
Chap 3-68
The Coefficient of Correlation
Using Microsoft Excel
Input data range and select appropriate options
Click OK to get output

DCOVA
Chap 3-69
Interpreting the Coefficient of Correlation
Using Microsoft Excel
r = .733
There is a relatively strong positive linear relationship between
test score #1 and test score #2.
Students who scored high on the first test tended to score high
on second test.
DCOVA

Chap 3-70
Pitfalls in Numerical
Descriptive Measures
Data analysis is objective
Should report the summary measures that best describe and
communicate the important aspects of the data set
Data interpretation is subjective
Should be done in fair, neutral and clear manner
DCOVA
Chap 3-71
Ethical Considerations
Numerical descriptive measures:
Should document both good and bad results
Should be presented in a fair, objective and neutral manner
Should not use inappropriate summary measures to distort facts
DCOVA

Chap 3-72
Chapter Summary
In this chapter we discussed
Measures of central tendency
Mean, median, mode, geometric mean
Measures of variation
Range, interquartile range, variance and standard deviation,
coefficient of variation, Z-scores
The shape of distributions
Skewness & Kurtosis
Describing data using the 5-number summary
Boxplots
Chap 3-73

Chapter Summary
Covariance and correlation coefficient
Pitfalls in numerical descriptive measures and ethical
considerations
(continued)
Chap 3-74
All rights reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying,
recording, or otherwise, without the prior written permission of
the publisher.
Printed in the United States of America.

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300,000$ Median300,000$
=MEDIAN(A2:A6)
100,000$ Mode100,000.00$ =MODE(A2:A6)
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Sheet1House PricesDescriptive Statistics$ 2,000,000Mean$
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Mean600000
Standard Error357770.8764
Median300000
Mode100000
Standard Deviation800000
Sample Variance640,000,000,000
Kurtosis4.1301
Skewness2.0068

Range1900000
Minimum100000
Maximum2000000
Sum3000000
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Statistics for Managers using Microsoft Excel® 7e Copyright
Chap 2-1
Chapter 2
Organizing and Visualizing Data
Statistics for Managers Using Microsoft Excel
7th Edition

Chap 2-2
Learning Objectives
In this chapter you learn:
To construct tables and charts for categorical data
To construct tables and charts for numerical data
The principles of properly presenting graphs
To organize and analyze many variables

Categorical Data Are Organized By Utilizing Tables
Chap 2-3
Categorical Data
Tallying Data
Summary Table
DCOVA
One Categorical Variable
Two Categorical Variables
Contingency Table
Chap 2-4
Organizing Categorical Data: Summary Table
A summary table tallies the frequencies or percentages of items
in a set of categories so that you can see differences between
categories. Banking Preference?PercentATM16%Automated or
live telephone2%Drive-through service at branch17%In person
at branch41%Internet24%
DCOVA
Summary Table From A Survey of 1000 Banking Customers

A Contingency Table Helps Organize Two or More Categorical
Variables
Used to study patterns that may exist between the responses of
two or more categorical variables
Cross tabulates or tallies jointly the responses of the categorical
variables
For two variables the tallies for one variable are located in the
rows and the tallies for the second variable are located in the
columns
Chap 2-5
DCOVA
Contingency Table - Example
A random sample of 400 invoices is drawn.

Each invoice is categorized as a small, medium, or large
amount.
Each invoice is also examined to identify if there are any errors.
This data are then organized in the contingency table to the
right.
Chap 2-6
DCOVANo
ErrorsErrorsTotalSmall
Amount17020190Medium
Amount10040140Large
Amount65570Total33565400
Contingency Table Showing
Frequency of Invoices Categorized
By Size and The Presence Of Errors
Contingency Table Based On Percentage Of Overall Total
Chap 2-7No
Amount10040140Large
DCOVANo

Amount42.50%5.00%47.50%Medium
Amount25.00%10.00%35.00%Large
Amount16.25%1.25%17.50%Total83.75%16.25%100.0%
42.50% = 170 / 400
25.00% = 100 / 400
16.25% = 65 / 400
83.75% of sampled invoices have no errors and 47.50% of
sampled invoices are for small amounts.
Contingency Table Based On Percentage of Row Totals
Chap 2-8No
Amount10040140Large
DCOVANo
Amount71.43%28.57%100.0%Large
Amount92.86%7.14%100.0%Total83.75%16.25%100.0%
89.47% = 170 / 190
71.43% = 100 / 140
92.86% = 65 / 70
Medium invoices have a larger chance (28.57%) of having
errors than small (10.53%) or large (7.14%) invoices.

Contingency Table Based On Percentage Of Column Totals
Chap 2-9No
Amount10040140Large
DCOVANo
Amount29.85%61.54%35.00%Large
Amount19.40%7.69%17.50%Total100.0%100.0%100.0%
50.75% = 170 / 335
30.77% = 20 / 65
There is a 61.54% chance that invoices with errors are of
medium size.

Chap 2-10
Tables Used For Organizing
Numerical Data
Numerical Data
Ordered Array
DCOVA
Cumulative
Distributions
Frequency
Distributions
Stacked Or Unstacked Format
This is an issue when you have a categorical variable that may
be used group your numerical variable for analysis.
Stacked format is when your numerical variable is in one
column and a second column identifies the value of the
categorical variable.

Unstacked format is when the values of the numerical variable
in each group (unique value of the categorical variable) are in
different columns.
Chap 2-11
Example of Stacked & Unstacked Format
Chap 2-12Stacked FormatUnstacked FormatAge OfDay orAge
OfAge OfStudentsNight StudentDay StudentsNight
Students16D161819D192322D221818N172823N191917D25321
9D171925D203318N2728N1817D2020D3227D19N32N18D20D
32D19N33N
Different Programs &
different analyses may
require a specific format

Chap 2-13
Organizing Numerical Data:
Ordered Array
An ordered array is a sequence of data, in rank order, from the
smallest value to the largest value.
Shows range (minimum value to maximum value)
May help identify outliers (unusual observations)Age of
Surveyed College StudentsDay
Students161717181818191920202122222527323842Night
Students181819192021232832334145
DCOVA
Chap 2-14
Frequency Distribution
The frequency distribution is a summary table in which the data
are arranged into numerically ordered classes.
You must give attention to selecting the appropriate number of
class groupings for the table, determining a suitable width of a
class grouping, and establishing the boundaries of each class
grouping to avoid overlapping.

The number of classes depends on the number of values in the
data. With a larger number of values, typically there are more
classes. In general, a frequency distribution should have at
least 5 but no more than 15 classes.
To determine the width of a class interval, you divide the range
(Highest value–Lowest value) of the data by the number of class
groupings desired.
DCOVA
Chap 2-15
Frequency Distribution Example
Example: A manufacturer of insulation randomly selects 20
winter days and records the daily high temperature
24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44,
27, 53, 27
DCOVA

Chap 2-16
Frequency Distribution Example
Sort raw data in ascending order:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44,
46, 53, 58
Find range: 58 - 12 = 46
Select number of classes: 5 (usually between 5 and 15)
Compute class interval (width): 10 (46/5 then round up)
Determine class boundaries (limits):
Class 1: 10 to less than 20
Compute class midpoints: 15, 25, 35, 45, 55
Count observations & assign to classes
DCOVA

Chap 2-17
Organizing Numerical Data: Frequency Distribution Example
Class Midpoints Frequency
10 but less than 20 15 3
Total 20
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44,
46, 53, 58
DCOVA
Chap 2-18
Organizing Numerical Data: Relative & Percent Frequency
Distribution Example

Class Frequency
10 but less than 20 3 .15
15%
30%
25%
20%
10%
Total 20 1.00
100%
Relative
Frequency
Percentage
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44,
46, 53, 58
DCOVA

Chap 2-19
Organizing Numerical Data: Cumulative Frequency Distribution
Example
Class
10 but less than 20 3 15% 3
15%
20 but less than 30 6 30% 9
45%
30 but less than 40 5 25% 14
70%
40 but less than 50 4 20% 18
90%
50 but less than 60 2 10% 20
100%
Total 20 100 20
100%
Percentage
Cumulative Percentage
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44,
46, 53, 58
Frequency
Cumulative Frequency
DCOVA

Chap 2-20
Why Use a Frequency Distribution?
It condenses the raw data into a more useful form
It allows for a quick visual interpretation of the data
It enables the determination of the major characteristics of the
data set including where the data are concentrated / clustered
DCOVA
Chap 2-21
Frequency Distributions:
Some Tips
Different class boundaries may provide different pictures for
the same data (especially for smaller data sets)
Shifts in data concentration may show up when different class
boundaries are chosen

As the size of the data set increases, the impact of alterations in
the selection of class boundaries is greatly reduced
When comparing two or more groups with different sample
sizes, you must use either a relative frequency or a percentage
distribution
DCOVA
Visualizing Categorical Data Through Graphical Displays
Chap 2-22
Categorical Data
Visualizing Data
Bar
Chart
Summary Table For One Variable
Contingency Table For Two Variables
Side By Side Bar Chart
DCOVA
Pie Chart
Pareto

Chart
Chap 2-23
Visualizing Categorical Data:
The Bar Chart
In a bar chart, a bar shows each category, the length of which
represents the amount, frequency or percentage of values falling
into a category which come from the summary table of the
variable.
DCOVABanking Preference?%ATM16%Automated or live
telephone2%Drive-through service at branch17%In person at
branch41%Internet24%
Chap 2-24

The Pie Chart
The pie chart is a circle broken up into slices that represent
categories. The size of each slice of the pie varies according to
the percentage in each category.
DCOVABanking Preference?%ATM16%Automated or live
telephone2%Drive-through service at branch17%In person at
branch41%Internet24%
Chap 2-25
The Pareto Chart
Used to portray categorical data (nominal scale)
A vertical bar chart, where categories are shown in descending
order of frequency
A cumulative polygon is shown in the same graph
Used to separate the “vital few” from the “trivial many”
DCOVA

Chap 2-26
The Pareto Chart (con’t)
DCOVA
Side By Side Bar Charts
Chap 2-27
The side by side bar chart represents the data from a
contingency table.
DCOVA
Invoices with errors are much more likely to be of
medium size (61.54% vs 30.77% and 7.69%)No
Amount29.85%61.54%35.00%Large

Amount19.40%7.69%17.50%Total100.0%100.0%100.0%
Invoice Size Split Out By Errors & No Errors
Small No Errors Errors 0.50700000000000001
0.30800000000000027 Medium No Errors Errors
0.29900000000000032 0.61600000000000055 Large
No Errors Errors 0.19400000000000017
7.6000000000000068E-2
Chap 2-28
Visualizing Numerical Data By Using Graphical Displays
Numerical Data
Ordered Array
Stem-and-Leaf
Display
Histogram
Polygon

Ogive
Frequency Distributions and
Cumulative Distributions
DCOVA
Chap 2-29
Stem-and-Leaf Display
A simple way to see how the data are distributed and where
concentrations of data exist
METHOD: Separate the sorted data series
into leading digits (the stems) and
the trailing digits (the leaves)
DCOVA

Chap 2-30
Stem and Leaf Display
A stem-and-leaf display organizes data into groups (called
stems) so that the values within each group (the leaves) branch
out to the right on each row.
StemLeaf1677888992001225732842
Age of College Students
Day Students Night
StudentsStemLeaf1889920138323415Age of Surveyed College
StudentsDay
Students161717181818191920202122222527323842Night
Students181819192021232832334145
DCOVA
Chap 2-31
Visualizing Numerical Data:
The Histogram
A vertical bar chart of the data in a frequency distribution is
called a histogram.
In a histogram there are no gaps between adjacent bars.
The class boundaries (or class midpoints) are shown on the

horizontal axis.
The vertical axis is either frequency, relative frequency, or
percentage.
The height of the bars represent the frequency, relative
frequency, or percentage.
DCOVA
Chap 2-32
The Histogram
Class Frequency
15
30
25
20

10
Total 20 1.00
100
Relative
Frequency
Percentage
(In a percentage histogram the vertical axis would be defined to
show the percentage of observations per class)
DCOVA
Chap 2-33
The Polygon
A percentage polygon is formed by having the midpoint of each
class represent the data in that class and then connecting the
sequence of midpoints at their respective class percentages.
The cumulative percentage polygon, or ogive, displays the
variable of interest along the X axis, and the cumulative
percentages along the Y axis.

Useful when there are two or more groups to compare.
DCOVA
Chap 2-34
The Frequency Polygon
Class Midpoints
Class
Frequency
Class Midpoint
(In a percentage polygon the vertical axis would be defined to
show the percentage of observations per class)

DCOVA
Chap 2-35
The Ogive (Cumulative % Polygon)
Class
% less
than lower
boundary
Lower class boundary
Lower Class Boundary
(In an ogive the percentage of the observations less than each
lower class boundary are plotted versus the lower class

boundaries.
DCOVA
Chap 2-36
Visualizing Two Numerical Variables By Using Graphical
Displays
Two Numerical Variables
Scatter Plot
Time-Series Plot
DCOVA

Chap 2-37
Visualizing Two Numerical Variables: The Scatter Plot
Scatter plots are used for numerical data consisting of paired
observations taken from two numerical variables
One variable is measured on the vertical axis and the other
variable is measured on the horizontal axis
Scatter plots are used to examine possible relationships between
two numerical variables
DCOVA
Chap 2-38
Scatter Plot ExampleVolume per dayCost per
day231252614029146331603816742170501885519560200
DCOVA

Chap 2-39
A Time-Series Plot is used to study patterns in the values of a
numeric variable over time
The Time-Series Plot:
Numeric variable is measured on the vertical axis and the time
period is measured on the horizontal axis
Visualizing Two Numerical Variables: The Time Series Plot
DCOVA
Chap 2-40
Time Series Plot Example
YearNumber of Franchises1996 431997 541998 601999
732000 822001 952002 1072003 992004 95
DCOVA

Chap 2-41
Guidelines For Developing Visualizations
Avoid chartjunk
Use the simplest possible visualization
Include a title
Label all axes
Include a scale for each axis if the chart contains axes
Begin the scale for a vertical axis at zero
Use a constant scale
DCOVA
Chap 2-42
Graphical Errors: Chart Junk
1960: $1.00
1970: $1.60
1980: $3.10
1990: $3.80

Minimum Wage
0
2
4
1960
1970
1980
1990
$
Good Presentation
DCOVA

Chap 2-43
Graphical Errors:
No Relative Basis
A’s received by students.
A’s received by students.
Bad Presentation
0
200
300
FR
SO
JR
SR
Freq.
10%

30%
FR
SO
JR
SR
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior
100
20%
0%
%
Good Presentation
DCOVA
Chap 2-44
Graphical Errors:
Compressing the Vertical Axis
Good Presentation
Quarterly Sales
Quarterly Sales
Bad Presentation

0
25
50
Q1
Q2
Q3
Q4
$
0
100
200
Q1
Q2
Q3
Q4
$
DCOVA

Chap 2-45
Graphical Errors: No Zero Point on the Vertical Axis
Monthly Sales
36
39
42
45
J
F
M
A
M
J
$
Graphing the first six months of sales
Monthly Sales
0
39

42
45
J
F
M
A
M
J
$
36
Good Presentations
Bad Presentation
DCOVA

In Excel It Is Easy To Inadvertently Create Distortions
Excel often will create a graph where the vertical axis does not
start at 0
Excel offers the opportunity to turn simple charts into 3-D
charts and in the process can create distorted images
Unusual charts offered as choices by excel will most often
create distorted images
Chap 2-46
Using Excel Pivot Tables To Organize & Visualize Many
Variables
A pivot table:
Summarizes variables as a multidimensional summary table
Allows interactive changing of the level of summarization and

formatting of the variables
Allows you to interactively “slice” your data to summarize
subsets of data that meet specified criteria
Can be used to discover possible patterns and relationships in
multidimensional data that simpler tables and charts would fail
to make apparent.
Chap 2-47
DCOVA
A Two Variable Contingency Table For The Retirement Funds
Data
Chap 2-48
There are many more growth funds of average
risk than of low or high risk
DCOVA

A Multidimensional Contingency Table Tallies Responses Of
Three or More Categorical Variables
Chap 2-49
Growth funds
risk pattern depends
on market
Value funds risk
risk pattern is
different from that of
growth funds.
DCOVA
Multidimensional Contingency Tables Can Include Numerical
Variables
Chap 2-50

This table displays average 10-year return with the
market cap collapsed or hidden from view
Value funds with low or high risk have a higher average 10
year return than growth funds with those risk levels
DCOVA
The Same Table With Market Cap Expanded Shows A More
Complicated Pattern
Chap 2-51
Growth funds with large market capitalizations are the poorest
performers and depress the average for growth fund category
DCOVA
Double-clicking A Cell Drills Down & Displays The Underlying
Data

Chap 2-52
Double-clicking in the cell where the joint response
“value fund and high risk” is tallied creates a new
worksheet where the details for all the funds that
meet this criteria are displayed
DCOVA
Pivot Tables, Slicers & Business Analytics
Many analytics processes start with many variables and let you
explore the data by use of filtering
In Excel, using slicers is one way to mimic this filtering
operation
Slicers can be used to filter any variable that is associated with
a Pivot Table
By clicking buttons in slicer panels you can subset and filter
data and visually see answers to questions
Chap 2-53
DCOVA

Chap 2-54
Chapter Summary
In this chapter we have:
Constructed tables and charts for categorical data
Constructed tables and charts for numerical data
Examined the principles of properly presenting graphs
Examined methods to organize and analyze many variables in
Excel
Chap 2-55
the publisher.

Banking Preference
0%5%10%15%20%25%30%35%40%45%
ATM
Automated or live telephone
Drive-through service at branch
In person at branch
Internet
Chart2ATMAutomated or live telephoneDrive-through service
at branchIn person at branchInternet
Percentage
Banking Preference
0.16
0.02
0.17
0.41
0.24
Banking Preference
0.16
0.02
0.17
0.41
0.24
Sheet1Banking PreferencePercentageATM16%Automated or

Sheet1
Percentage
Banking Preference
Sheet2
Banking Preference
Sheet3
Banking Preference
16%
2%
17%
41%
24%
ATM
Automated or live
telephone
Drive-through service at
branch
In person at branch
Internet
Banking Preference
0.16
0.02
0.17
0.41
0.24
Sheet1Banking PreferencePercentageATM16%Automated or
Sheet1
Percentage
Banking Preference
Sheet2
Banking Preference

Sheet3
Pareto Chart For Banking Preference
0%
20%
40%
60%
80%
100%
In person
at branch
InternetDrive-
through
service at
branch
ATMAutomated
or live
telephone
% in each category
(bar graph)
0%
20%
40%
60%
80%
100%
Cumulative %
(line graph)
0246851525354555MoreFrequencyHistogram: Age Of Students
Chart251525354555More
Frequency
Frequency
Histogram: Age Of Students
0
3
6

5
4
2
0
Sheet4BinFrequency105200300400500More0
Sheet5
Frequency
Bin
Frequency
Histogram
Sheet6BinFrequencyCumulative %BinFrequencyCumulative
%50.00%35630.00%15210.00%45555.00%25430.00%25475.00
%35660.00%15285.00%45585.00%55295.00%55295.00%65110
0.00%651100.00%50100.00%More0100.00%More0100.00%
Sheet6
Frequency
Cumulative %
Bin
Frequency
Histogram
Sheet7
Frequency
Frequency
Histogram
Sheet8
Frequency
Frequency
Histogram
Sheet9
Frequency
Bin
Frequency

Histogram
Sheet10
Sheet11BinFrequency9.9319.9620.9130.9440.9450.92More0
Sheet11
Frequency
Bin
Frequency
Histogram
Sheet12
Frequency
Frequency
Histogram
Sheet229.9319.9729.91139.91249.91459.9161717202125272831
3334364348
Sheet3103206305404502
012345675152535455565FrequencyFrequency Polygon: Age Of
Students
Chart35152535455565
Frequency
Frequency
Frequency Polygon: Age Of Students
0
3
6
5
4
2
0
Sheet5
Frequency
Bin
Frequency
Histogram

%50.00%35630.00%15210.00%45555.00%25430.00%25475.00
%35660.00%15285.00%45585.00%55295.00%55295.00%65110
0.00%651100.00%50100.00%More0100.00%More0100.00%
Sheet6
Frequency
Cumulative %
Bin
Frequency
Histogram
Sheet7BinFrequency50153256355454552650
Sheet7
Frequency
Frequency
Histogram
Sheet8
Frequency
Sheet9
Frequency
Frequency
Histogram
Sheet10
Frequency
Bin
Frequency
Histogram
Sheet11
Sheet12
Frequency
Bin
Frequency
Histogram

Sheet2
Frequency
Frequency
Histogram
Sheet329.9319.9729.91139.91249.91459.9161717202125272831
3334364348
103206305404502
020406080100102030405060
Ogive: Age Of Students
Chart1102030405060
Frequency
Ogive: Age Of Students
0
15
45
70
90
100
Sheet5
Frequency
Bin
Frequency
Histogram
%50.00%35630.00%15210.00%45555.00%25430.00%25475.00
%35660.00%15285.00%45585.00%55295.00%55295.00%65110
0.00%651100.00%50100.00%More0100.00%More0100.00%
Sheet6
Frequency
Cumulative %
Bin
Frequency

Histogram
Sheet7BinFrequency100201530454070509060100
Sheet7
Frequency
Sheet8
Frequency
Ogive
Sheet9
Frequency
Frequency
Histogram
Sheet10
Frequency
Bin
Frequency
Histogram
Sheet11
Sheet12
Frequency
Bin
Frequency
Histogram
Sheet2
Frequency
Frequency
Histogram
Sheet329.9319.9729.91139.91249.91459.9161717202125272831
3334364348
103206305404502
Cost per Day vs. Production Volume
0
50

100
150
200
250
203040506070
Volume per Day
Cost per Day
Chart2232629333842505560
Cost per day
Volume per Day
Cost per Day
Cost per Day vs. Production Volume
125
140
146
160
167
170
188
195
200
Sheet1Volume per dayCost per
day231252614029146331603816742170501885519560200
Sheet1000000000
Cost per day
Volume per Day
Cost per Day
Production Volume vs. Cost per Day
0
0
0
0
0
0
0
0

0
Sheet2
Sheet3
Number of Franchises, 1996-2004
0
20
40
60
80
100
120
1994199619982000200220042006
Year
Number of
Franchises
Chart2199619971998199920002001200220032004
Number of Franchises
Year
43
54
60
73
82
95
107
99
95
Sheet1YearNumber of
Franchises19964319975419986019997320008220019520021072
00399200495
Sheet1199619971998199920002001200220032004
Year

43
54
60
73
82
95
107
99
95
Sheet2
Sheet3
Chap 1-1
Statistics for Managers Using Microsoft Excel®
7th Edition
Chapter 1
Defining & Collecting Data

Chap 1-2
Learning Objectives
In this chapter you learn:
The types of variables used in statistics
The measurement scales of variables
How to collect data
The different ways to collect a sample
About the types of survey errors
Types of Variables
Categorical (qualitative) variables have values that can only be
placed into categories, such as “yes” and “no.”
Numerical (quantitative) variables have values that represent
quantities.
Discrete variables arise from a counting process
Continuous variables arise from a measuring process

Chap 1-3
DCOVA
Types of Variables
Chap 1-4
Variables
Categorical
Numerical
Discrete
Continuous
Examples:
Marital Status
Political Party
Eye Color
(Defined categories)
Examples:
Number of Children
Defects per hour
(Counted items)
Examples:
Weight

Voltage
(Measured characteristics)
DCOVA
Levels of Measurement
A nominal scale classifies data into distinct categories in
which no ranking is implied.
Chap 1-5
Categorical Variables Categories
Personal Computer Ownership
Type of Stocks Owned
Internet Provider
Yes / No
AT&T, Verizon, Time Warner Cable
Growth / Value / Other

DCOVA
Levels of Measurement (con’t.)
An ordinal scale classifies data into distinct categories in
which ranking is implied
Chap 1-6
Categorical Variable Ordered Categories
Student class designationFreshman, Sophomore, Junior,
SeniorProduct satisfactionSatisfied, Neutral, UnsatisfiedFaculty
rankProfessor, Associate Professor, Assistant Professor,
InstructorStandard & Poor’s bond ratingsAAA, AA, A, BBB,
BB, B, CCC, CC, C, DDD, DD, DStudent GradesA, B, C, D, F
DCOVA

Levels of Measurement (con’t.)
An interval scale is an ordered scale in which the difference
between measurements is a meaningful quantity but the
measurements do not have a true zero point.
A ratio scale is an ordered scale in which the difference
between the measurements is a meaningful quantity and the
measurements have a true zero point.
Chap 1-7
DCOVA
Interval and Ratio Scales
Chap 1-8

DCOVA
Establishing A Business Objective Focuses Data Collection
Examples Of Business Objectives:
A marketing research analyst needs to assess the effectiveness
of a new television advertisement.
A pharmaceutical manufacturer needs to determine whether a
new drug is more effective than those currently in use.
An operations manager wants to monitor a manufacturing
process to find out whether the quality of the product being
manufactured is conforming to company standards.
An auditor wants to review the financial transactions of a
company in order to determine whether the company is in
compliance with generally accepted accounting principles.
Chap 1-9
DCOVA

Sources of Data
Primary Sources: The data collector is the one using the data for
analysis
Data from a political survey
Data collected from an experiment
Observed data
Secondary Sources: The person performing data analysis is not
the data collector
Analyzing census data
Examining data from print journals or data published on the
internet.
Chap 1-10
DCOVA
Sources of data fall into five categories
Data distributed by an organization or an individual
A designed experiment

A survey
An observational study
Data collected by ongoing business activities
Chap 1-11
DCOVA
Examples Of Data Distributed By Organizations or Individuals
Financial data on a company provided by investment services.
Industry or market data from market research firms and trade
associations.
Stock prices, weather conditions, and sports statistics in daily
newspapers.
Chap 1-12
DCOVA

Examples of Data From A Designed Experiment
Consumer testing of different versions of a product to help
determine which product should be pursued further.
Material testing to determine which supplier’s material should
be used in a product.
Market testing on alternative product promotions to determine
which promotion to use more broadly.
Chap 1-13
DCOVA
Examples of Survey Data
Political polls of registered voters during political campaigns.
People being surveyed to determine their satisfaction with a
recent product or service experience.

Chap 1-14
DCOVA
Examples of Data Collected From Observational Studies
Market researchers utilizing focus groups to elicit unstructured
responses to open-ended questions.
Measuring the time it takes for customers to be served in a fast
food establishment.
Measuring the volume of traffic through an intersection to
determine if some form of advertising at the intersection is
justified.
Chap 1-15
DCOVA

Examples of Data Collected From Ongoing Business Activities
A bank studies years of financial transactions to help them
identify patterns of fraud.
Economists utilize data on searches done via Google to help
forecast future economic conditions.
Marketing companies use tracking data to evaluate the
effectiveness of a web site.
Chap 1-16
DCOVA
Chap 1-17
Data Is Collected From Either A Population or A
SamplePOPULATION
A population consists of all the items or individuals about
which you want to draw a conclusion. The population is the
“large group”
SAMPLE
A sample is the portion of a population selected for analysis.

The sample is the “small group”
DCOVA
Chap 1-18
Population vs. Sample
Population
Sample
All the items or individuals about which you want to draw
conclusion(s)
A portion of the population of items or individuals

Data Cleaning Is Often A Necessary Activity When Collecting
Data
Often find “irregularities” in the data
Typographical or data entry errors
Values that are impossible or undefined
Missing values
Outliers
When found these irregularities should be reviewed
Many statistical software packages will handle irregularities in
an automated fashion (Excel does not)
Chap 1-19
Chap 1-20
A Sampling Process Begins With A Sampling Frame
The sampling frame is a listing of items that make up the
population
Frames are data sources such as population lists, directories, or
maps
Inaccurate or biased results can result if a frame excludes
certain portions of the population
Using different frames to generate data can lead to dissimilar
conclusions

DCOVA
Chap 1-21
Types of Samples
Samples
Non-Probability Samples
Judgment
Probability Samples
Simple
Random
Systematic
Stratified
Cluster
Convenience

DCOVA
Chap 1-22
Types of Samples:
Nonprobability Sample
In a nonprobability sample, items included are chosen without
regard to their probability of occurrence.
In convenience sampling, items are selected based only on the
fact that they are easy, inexpensive, or convenient to sample.
In a judgment sample, you get the opinions of pre-selected
experts in the subject matter.
DCOVA

Chap 1-23
Types of Samples:
Probability Sample
In a probability sample, items in the sample are chosen on the
basis of known probabilities.
Probability Samples
Simple
Random
Systematic
Stratified
Cluster
DCOVA
Chap 1-24
Probability Sample:
Simple Random Sample
Every individual or item from the frame has an equal chance of
being selected

Selection may be with replacement (selected individual is
returned to frame for possible reselection) or without
replacement (selected individual isn’t returned to the frame).
Samples obtained from table of random numbers or computer
random number generators.
DCOVA
Chap 1-25
Selecting a Simple Random Sample Using A Random Number
Table
Sampling Frame For Population With 850 Items
Item Name Item #
Bev R. 001
Ulan X. 002
. .
. .
. .
. .
Joann P. 849
Paul F. 850
Portion Of A Random Number Table

49280 88924 35779 00283 81163 07275
11100 02340 12860 74697 96644 89439
09893 23997 20048 49420 88872 08401
The First 5 Items in a simple random sample
Item # 492
Item # 808
Item # 892 -- does not exist so ignore
Item # 435
Item # 779
Item # 002
DCOVA
Chap 1-26
Decide on sample size: n
Divide frame of N individuals into groups of k individuals:
k=N/n
Randomly select one individual from the 1st group
Select every kth individual thereafter
Probability Sample:
Systematic Sample
N = 40
n = 4
k = 10
First Group

DCOVA
Chap 1-27
Probability Sample:
Stratified Sample
Divide population into two or more subgroups (called strata)
according to some common characteristic
A simple random sample is selected from each subgroup, with
sample sizes proportional to strata sizes
Samples from subgroups are combined into one
This is a common technique when sampling population of
voters, stratifying across racial or socio-economic lines.
Population
Divided
into 4
strata

DCOVA
Chap 1-28
Probability Sample
Cluster Sample
Population is divided into several “clusters,” each
representative of the population
A simple random sample of clusters is selected
All items in the selected clusters can be used, or items can be
chosen from a cluster using another probability sampling
technique
A common application of cluster sampling involves election exit
polls, where certain election districts are selected and sampled.
Population divided into 16 clusters.
Randomly selected clusters for sample

DCOVA
Chap 1-29
Probability Sample:
Comparing Sampling Methods
Simple random sample and Systematic sample
Simple to use
May not be a good representation of the population’s underlying
characteristics
Stratified sample
Ensures representation of individuals across the entire
population
Cluster sample
More cost effective
Less efficient (need larger sample to acquire the same level of
precision)
DCOVA

Chap 1-30
Evaluating Survey Worthiness
What is the purpose of the survey?
Is the survey based on a probability sample?
Coverage error – appropriate frame?
Nonresponse error – follow up
Measurement error – good questions elicit good responses
Sampling error – always exists
DCOVA
Chap 1-31
Types of Survey Errors
Coverage error or selection bias
Exists if some groups are excluded from the frame and have no
chance of being selected
Nonresponse error or bias
People who do not respond may be different from those who do
respond
Sampling error
Variation from sample to sample will always exist
Measurement error
Due to weaknesses in question design, respondent error, and
interviewer’s effects on the respondent (“Hawthorne effect”)

DCOVA
Chap 1-32
Types of Survey Errors
Coverage error
Nonresponse error
Sampling error
Measurement error
Excluded from frame
Follow up on nonresponses
Random differences from sample to sample
Bad or leading question
(continued)
DCOVA

Chap 1-33
Chapter Summary
In this chapter we have discussed:
The types of variables used in statistics
The measurement scales of variables
How to collect data
The different ways to collect a sample
The types of survey errors
the publisher.

Chap 1-34
DataCopy6Age2922242524222727254422342621252332253324
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Frequency Polygon
Age -- 25 35 45 55 0 0 17 3 1 1 0
Pctage_Polygon
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0.13636363636363635 4.5454545454545456E-2
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-- 25 35 45 55 0 17 3 1 1
Midpoints
Frequency
DataCopy3Age2922242524222727254422342621252332253324
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Freq_Polygon2
Frequency Polygon
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F -- 25 35 45 55 0 0 10 1 0 0
0
Pctage_Polygon2
Percentage Polygon
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9.0909090909090912E-2 0 0 0
CPctage_Polygon2
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59.99 0 0 0.63636363636363635
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19.989999999999998 29.99 39.99 49.99
59.99 0 0 0.90909090909090906 1 1 1

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Midpoints
Frequency
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Histogram of F
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Midpoints
Frequency
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22 22 22 2 2.5 3 23 23 23 2 2.5 3 24
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Pie Chart
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Pareto
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0.13636363636363635 4.5454545454545456E-2
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Frequency

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470003703
Case Analysis (75 points)
For the following Ducks Agency case, prepare a managerial
report (10 points) that addresses the case Assignment on page 6
of this exam, and that answers all case questions on page 8.
Merely answering the case questions without a report is not
acceptable and will result in score reduction. Finally, please
attach all charts, graphs and tables used to make your
conclusions and recommendations.

The Ducks Agency
The Ducks Agency (TDA) is a small advertising agency in
Portland, Oregon that helps clients get the biggest return on
their advertising dollars. TDA specializes in working with
companies that are looking to advertise their products and
services for the first time. Such companies are typically newer
businesses that have begun to grow and now have the revenues
to take the next step by investing in advertising. TDA has a
good track record of helping these companies feel comfortable
with their expenditure of advertising dollars. As pointed out by
Donalda Ducks, founder and CEO of this agency, the costs
incurred with advertising can be considerable and are always
perceived as a relatively high percentage of clients' revenues.
For first-time clients, the thought of investing in advertising, no
matter how much sense it might make, always leads to questions
about whether the expense will be worth the investment
Companies like TDA typically try to identify the particular
market segments that are most likely to buy their clients goods
and services and then locate an advertising outlet that will reach
this particular market group. Client groups require considerable
explanation about how this "matching" occurs. Donalda Ducks
typically explains it like this:
We collect a lot of information on clients' actual sales over a
two to three month period and on the people who make those
purchases. We get this information from a variety of sources,
including surveys, interviews, credit records, mailing lists,
contests, and so forth. Our goal is to learn as much as we can
about our clients' customers to see whether there might be a
distinct “profile” of the typical customer for a particular
product o r service. If a distinct profile emerges from our
research, then we try to match that profile to advertising outlets,
such as TV, radio, newspapers, and magazines known to be
watched, listened to or read by people with this particular
profile. In this way, we target advertising directly to high
potential customers. This procedure goes a long way in helping

our clients feel more comfortable that at least the money spent
on advertising is putting their products and services in front of
the right audience. We've been doing it this way for years and
have a long track record of being successful.
TDA recently signed a new client, Cycle Emporium, in nearby
Seattle. Cycle Emporium markets, under its own name, three
lines of racing and mountain bikes, made by several bicycle
manufacturers. Cycle Emporium currently sells its bikes in their
six retail outlets in major cities throughout the Northwest.
Cycle Emporium is now ready to launch a direct sales campaign
of their products by advertising bicycles in nationally
distributed magazines.
This direct sales effort will rely on reaching potential customers
by placing half-page, two-color ads in popular magazines that
have large national subscription bases. The marketing campaign
would attempt to (1) create name recognition for Cycle
Emporium's products based on placing five ads in each issue of
chosen magazines and (2) offer customers savings that result
from eliminating the “middle-man.” Thus, it is clear that
choosing target magazines for each product is crucial in order to
insure that Cycle Emporium's new venture will be successful.
They have set aside $240,000 to advertise their products in this
manner. In addition to the costs of placing the ads, this budget
must also cover TDA’s separate charges to Cycle Emporium for
the creation and production of the advertising copy as well as
their fee and overhead charges. Choosing the wrong magazine
not only means that this total budget is being spent on multiple
ads to reach the wrong audience, but that the real potential
customers would still go unreached.
Cycle Emporium sells three lines of bicycles. The lower line
includes "basic" racing and mountain bikes. These bicycles,
made by the largest bicycle manufacturer in the U.S., tend to be
heavy as far as bikes go, have relatively few features and offer
few customer options. Their middle line, made by a popular
West Coast manufacturer, includes bicycles that are made of
light- weight metals with many features that serious bikers want

and that provide a modest number of options to help buyers
customize their bikes. The upper line is made by one of
Europe's leading bicycle manufacturers, and includes bicycles
that are made of ultra-light alloy metals with all the "bells and
whistles" which can be put on a bike. Customers are allowed to
choose among a number of options to customize their purchases
from the upper line of bicycles.
Donalda Ducks put together a market research team to identify
the profile of the typical customer for each product line. To do
so, the market research team collected information from persons
who purchased bicycles at Cycle Emporium's six retail stores. A
random sample of customers during a two-month period was
asked to complete a short survey that contained descriptive
questions about themselves. To encourage customers to
complete the survey, each was offered as a gift for their
participation, a biker's helmet, a mileage meter, or a bicycle tire
pump. Over 90 percent of the sampled customers completed the
survey. Questions were chosen to get an understanding of the
demographic background (i.e., age, gender, marital status,
education) and the interest level in biking (i.e., extent of use,
fitness level, self-rated interest) of customers.
Based on these data, a profile of the “ typical” customer for
each product line of merchandise needed to be created and
compared to the “typical” subscriber profile for a list of
magazines. The list of potential magazines was chosen to reflect
three issues: (a) the subscriber base needed to be a national one,
(b) the subscriber list needed to fall in the moderate size
category for nationally- distributed magazines, and (c) the
magazine needed to focus on a particular topic or theme.
Cycle Emporium very specifically wanted to reach a national
market in their first attempt to enter the direct sales arena. They
reasoned that this was the best way to guard against the
problems created by unpredictable, cyclical, regional economic
downturns. The choice of looking at magazines in the moderate-
sized national subscription base would mean that ads would be
similar in costs and within Cycle Emporium’s advertising

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