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Data and Data Sets
Data are the facts and figures collected, analyzed,
and summarized for presentation and interpretation. All the data collected in a particular study are referred
to as the data set for the study.
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Stock Annual Earn/Exchange Sales($M) Share($)
Data, Data Sets, Elements, Variables, and Observations
Company
Dataram EnergySouth Keystone LandCare Psychemedics
NQ 73.10 0.86 N 74.00 1.67 N 365.70 0.86 NQ 111.40 0.33 N 17.60 0.13
Variables
Element
Names
Data Set
Observation
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Data can be further classified as being qualitative or quantitative. Data can be further classified as being qualitative or quantitative.
The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative.
The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative.
In general, there are more alternatives for statistical analysis when the data are quantitative. In general, there are more alternatives for statistical analysis when the data are quantitative.
Qualitative and Quantitative Data
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Qualitative Data
Labels or names used to identify an attribute of each element Labels or names used to identify an attribute of each element
Often referred to as categorical data Often referred to as categorical data
Use either the nominal or ordinal scale of measurement Use either the nominal or ordinal scale of measurement
Can be either numeric or nonnumeric Can be either numeric or nonnumeric
Appropriate statistical analyses are rather limited Appropriate statistical analyses are rather limited
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Quantitative Data
Quantitative data indicate how many or how much: Quantitative data indicate how many or how much:
discrete, if measuring how many discrete, if measuring how many
continuous, if measuring how much continuous, if measuring how much
Quantitative data are always numeric. Quantitative data are always numeric.
Ordinary arithmetic operations are meaningful for quantitative data. Ordinary arithmetic operations are meaningful for quantitative data.
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Descriptive Statistics
Most of the statistical information in newspapers, magazines, company reports, and other publications consists of data that are summarized and presented in a form that is easy to understand. Such summaries of data, which may be tabular, graphical, or numerical, are referred to as descriptive statistics.
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Example: Hudson Auto Repair
The manager of Hudson Autowould like to have a betterunderstanding of the costof parts used in the enginetune-ups performed in theshop. She examines 50customer invoices for tune-ups. The costs of
parts,rounded to the nearest dollar, are listed on the
nextslide.
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Example: Hudson Auto Repair
Sample of Parts Cost ($) for 50 Tune-ups
91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73
91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73
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Tabular Summary: Frequency and Percent Frequency
50-59 60-69 70-79 80-89 90-99 100-109
2 13 16 7 7 5 50
4 26 32 14 14 10 100
(2/50)100(2/50)100
Parts Cost ($)
Parts Frequency
PercentFrequency
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Graphical Summary: Histogram
22
44
66
88
1010
1212
1414
1616
1818
PartsCost ($) PartsCost ($)
Fre
qu
en
cy
Fre
qu
en
cy
50-59 60-69 70-79 80-89 90-99 100-11050-59 60-69 70-79 80-89 90-99 100-110
Tune-up Parts CostTune-up Parts Cost
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Numerical Descriptive Statistics
Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing the 50 cost values and then dividing by 50).
The most common numerical descriptive statistic is the average (or mean).
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Statistical Inference
PopulationPopulation
SampleSample
Statistical inferenceStatistical inference
CensusCensus
Sample surveySample survey
- the set of all elements of interest in a particular study
- a subset of the population
- the process of using data obtained from a sample to make estimates and test hypotheses about the characteristics of a population
- collecting data for a population
- collecting data for a sample
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Process of Statistical Inference
1. Population consists of all
tune-ups. Averagecost of parts is
unknown.
1. Population consists of all
tune-ups. Averagecost of parts is
unknown.
2. A sample of 50engine tune-ups
is examined.
2. A sample of 50engine tune-ups
is examined.
3. The sample data provide a sample
average parts costof $79 per tune-up.
3. The sample data provide a sample
average parts costof $79 per tune-up.
4. The sample averageis used to estimate the population average.
4. The sample averageis used to estimate the population average.
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Statistical Analysis Using Microsoft Excel
Statistical analysis typically involves working with large amounts of data. Computer software is typically used to conduct the analysis. Frequently the data that is to be analyzed resides in a spreadsheet.
Modern spreadsheet packages are capable of data management, analysis, and presentation. MS Excel is the most widely available spreadsheet software in business organizations.
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Statistical Analysis Using Microsoft Excel
3 tasks might be needed:• Enter Data
• Enter Functions and Formulas• Apply Tools
A
1Parts Cost
2 913 714 1045 856 627 788 69
D EMean =AVERAGE(A2:A71)
Median =MEDIAN(A2:A71)Mode =MODE(A2:A71)
Range =MAX(A2:A71)-MIN(A2:A71)
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Excel Worksheet (showing data)
Note: Rows 10-51 are not shown.
Statistical Analysis Using Microsoft Excel
A B C D
1 Customer Invoice #Parts
Cost ($)Labor
Cost ($)2 Sam Abrams 20994 91 1853 Mary Gagnon 21003 71 2054 Ted Dunn 21010 104 1925 ABC Appliances 21094 85 1786 Harry Morgan 21116 62 2427 Sara Morehead 21155 78 1488 Vista Travel, Inc. 21172 69 1659 John Williams 21198 74 190
A B C D
1 Customer Invoice #Parts
Cost ($)Labor
Cost ($)2 Sam Abrams 20994 91 1853 Mary Gagnon 21003 71 2054 Ted Dunn 21010 104 1925 ABC Appliances 21094 85 1786 Harry Morgan 21116 62 2427 Sara Morehead 21155 78 1488 Vista Travel, Inc. 21172 69 1659 John Williams 21198 74 190
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Excel Formula Worksheet
Note: Columns A-B and rows 10-51 are not shown.
Statistical Analysis Using Microsoft Excel
C D E F G
1Parts
Cost ($)Labor
Cost ($)2 91 185 Average Parts Cost =AVERAGE(C2:C51)3 71 2054 104 1925 85 1786 62 2427 78 1488 69 1659 74 190
C D E F G
1Parts
Cost ($)Labor
Cost ($)2 91 185 Average Parts Cost =AVERAGE(C2:C51)3 71 2054 104 1925 85 1786 62 2427 78 1488 69 1659 74 190
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Excel Value Worksheet
Note: Columns A-B and rows 10-51 are not shown.
Statistical Analysis Using Microsoft Excel
C D E F G
1Parts
Cost ($)Labor
Cost ($)2 91 185 Average Parts Cost 793 71 2054 104 1925 85 1786 62 2427 78 1488 69 1659 74 190
C D E F G
1Parts
Cost ($)Labor
Cost ($)2 91 185 Average Parts Cost 793 71 2054 104 1925 85 1786 62 2427 78 1488 69 1659 74 190
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A frequency distribution is a tabular summary of data showing the frequency (or number) of items in each of several non-overlapping classes.
A frequency distribution is a tabular summary of data showing the frequency (or number) of items in each of several non-overlapping classes.
The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data.
The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data.
Ch. 2: Summarizing Qualitative DataFrequency Distribution
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Guests staying at Marada Inn were asked to rate the
quality of their accommodations as being excellent,
above average, average, below average, or poor. The
ratings provided by a sample of 20 guests are: Above Average Below Average Above Average Average Average Above Average Above Average
Average Above Average Below Average Poor Excellent Above Average Average
Above Average Above Average Below Average Poor Above Average Average
Frequency Distribution
Example: Marada Inn
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Frequency Distribution
PoorBelow AverageAverageAbove AverageExcellent
2 3 5 9 1
Total 20
Rating Frequency
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Using Excel’s COUNTIF Functionto Construct a Frequency Distribution
Excel Formula Worksheet
Note: Rows 9-21 are not shown.
A B C D1 Quality Rating Quality Rating Frequency2 Above Average Poor =COUNTIF($A$2:$A$21,C2)3 Below Average Below Average =COUNTIF($A$2:$A$21,C3)4 Above Average Average =COUNTIF($A$2:$A$21,C4)5 Average Above Average =COUNTIF($A$2:$A$21,C5)6 Average Excellent =COUNTIF($A$2:$A$21,C6)7 Above Average Total =SUM(D2:D6)8 Above Average
Download Ch01-Ch02-CustomerRatings.xlsx
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Excel Value Worksheet
Using Excel’s COUNTIF Functionto Construct a Frequency Distribution
Note: Rows 9-21 are not shown.
A B C D1 Quality Rating Quality Rating Frequency2 Above Average Poor 23 Below Average Below Average 34 Above Average Average 55 Average Above Average 96 Average Excellent 17 Above Average Total 208 Above Average
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The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class.
The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class.
A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class.
A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class.
Relative Frequency Distribution
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Percent Frequency Distribution
The percent frequency of a class is the relative frequency multiplied by 100. The percent frequency of a class is the relative frequency multiplied by 100.
A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class.
A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class.
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Relative Frequency andPercent Frequency Distributions
PoorBelow AverageAverageAbove AverageExcellent
.10 .15 .25 .45 .05
Total 1.00
10 15 25 45 5 100
RelativeFrequency
PercentFrequencyRating
.10(100) = 10
.10(100) = 10
1/20 = .051/20 = .05
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Excel Formula Worksheet
Note: Columns A-B and rows 9-21 and are not shown.
Using Excel to Construct Relative Frequency and Percent Frequency
Distributions
C D E F
1 Quality Rating FrequencyRelative
FrequencyPercent
Frequency2 Poor =COUNTIF($A$2:$A$21,C2) =D2/$D$7 =E2*1003 Below Average =COUNTIF($A$2:$A$21,C3) =D3/$D$7 =E3*1004 Average =COUNTIF($A$2:$A$21,C4) =D4/$D$7 =E4*1005 Above Average =COUNTIF($A$2:$A$21,C5) =D5/$D$7 =E5*1006 Excellent =COUNTIF($A$2:$A$21,C6) =D6/$D$7 =E6*1007 Total =SUM(D2:D6) =SUM(E2:E6) =SUM(F2:F6)8
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Excel Value Worksheet
Using Excel to Construct Relative Frequency and Percent Frequency
Distributions
C D E F
1 Quality Rating FrequencyRelative
FrequencyPercent
Frequency2 Poor 2 0.10 103 Below Average 3 0.15 154 Average 5 0.25 255 Above Average 9 0.45 456 Excellent 1 0.05 57 Total 20 1.00 1008
Note: Columns A-B and rows 9-21 and are not shown.
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