Descriptive Statistics

Overview of Using Data

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Business Analytics

Lecture # 02

TOPICS to be COVERED

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Overview of Using Data: Definitions and Goals

• Data
• Variable
• Observation
• Variation
• Random variables

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• Data are the facts and figures collected, analyzed, and summarized for presentation and interpretation.
• A characteristic or a quantity of interest that can take on different values is known as a variable.

Example: Height of a whole class students

• An observation is a set of values corresponding to a set of variables

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variation is the difference in a variable measured over observations (time, customers, items, etc.).

Example: When we collect data, we are gathering past observed values, or realizations of a variable. By collecting these past realizations of one or more variables, our goal is to learn more about the variation of a particular business situation.

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The role of descriptive analytics is to collect and analyse data to gain a better understanding of variation and its impact on the business setting.

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The values of some variables are under direct control of the decision maker (these are often called decision variables).

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The values of other variables may fluctuate with uncertainty because of factors outside the direct control of the decision maker. In general, a quantity whose values are not known with certainty is called a random variable, or uncertain variable.

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Types of data

• Population and Sample Data
• Quantitative and Categorical Data
• Cross-Sectional and Time Series Data

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Data can be categorized in several ways based on how they are collected and the type collected.

• In many cases, it is not feasible to collect data from the population of all elements of interest. In such instances, we collect data from a subset of the population known as a sample.

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What is a Statistic????

Population

Sample

Sample

Sample

Sample

Parameter: value that describes a population

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Statistic: a value that describes a sample

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Quantitative and Categorical Data�

Data are considered quantitative data if

numeric and arithmetic operations included ,

such as

• addition,
• subtraction,
• multiplication,
• and division.

For instance, we can sum the values for Volume in the Dow data in Table 2.1 to calculate a total volume of all shares traded by companies included in the Dow.

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• If arithmetic operations cannot be performed on the data, they are considered categorical data
• For instance, the data in the Industry column in Table 2.1 are categorical

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Cross-Sectional and Time Series Data

• Cross-sectional data are collected from several entities at the same, or approximately the same, point in time.

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The data in Table 2.1 are cross-sectional because they describe the 30 companies that comprise the Dow at the same point in time (July 2015).

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• Time series data are collected over several time periods.

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Graphs of time series data are frequently found in business and economic publications.

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Some Definitions

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Variable - any characteristic of an individual or entity. A variable can take different values for different individuals. Variables can be categorical or quantitative. Per S. S. Stevens…

• Nominal - Categorical variables with no inherent order or ranking sequence such as names or classes (e.g., gender). Value may be a numerical, but without numerical value (e.g., I, II, III). The only operation that can be applied to Nominal variables is listing.

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• Ordinal - Variables with an inherent rank or order, e.g. mild, moderate, severe. Can be compared for equality, or greater or less, but not how much greater or less.

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Some Definitions

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• Interval - Values of the variable are ordered as in Ordinal, and additionally, differences between values are meaningful, however, the scale is not absolutely anchored. Calendar dates and temperatures on the Fahrenheit scale are examples. Addition and subtraction, but not multiplication and division are meaningful operations.

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• Ratio - Variables with all properties of Interval plus an absolute, non-arbitrary zero point, e.g. age, weight, temperature (Kelvin). Addition, subtraction, multiplication, and division are all meaningful operations.

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Types of measurement

• When collecting or gathering data we collect data from individuals cases on particular variables.
• A variable is a unit of data collection whose value can vary.
• Variables can be defined into types according to the level of mathematical scaling that can be carried out on the data.
• There are four types of data or levels of measurement:

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Categorical (Nominal) data�

• What does this mean? No mathematical operations can be performed on the data relative to each other.
• Therefore, nominal data reflect qualitative differences rather than quantitative ones.
• Nominal measurements only permit you to determine whether two individuals are the same or different.

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Examples:

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Nominal data

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Ordinal data�

• Ordinal data is data that comprises of categories that can be rank ordered.
• Similarly with nominal data the distance between each category cannot be calculated but the categories can be ranked above or below each other.
• No fixed units of measurement
• Examples:
• - college football rankings
• - survey responses

(poor, average, good, very good, excellent)

• What does this mean? Can make statistical judgements and perform limited maths.

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Ordinal data�

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Interval and Ratio data�

• Both interval and ratio data are examples of scale data.
• Scale data:
• data is in numeric format ($50, $100, $150)
• data that can be measured on a continuous scale
• the distance between each can be observed and as a result measured
• the data can be placed in rank order.

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Interval data�

• Ordinal data but with constant differences between observations
• Examples:
• Time – moves along a continuous measure or seconds, minutes and so on and is without a zero point of time.
• Temperature – moves along a continuous measure of degrees and is without a true zero.
• SAT scores

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Ratios

• Ratio data measured on a continuous scale and does have a natural zero point
• Ratios are meaningful
• Examples:
• Monthly sales
• Delivery times
• Weight
• Height
• Age

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Data for Business Analytics

Classifying Data Elements in a Purchasing Database

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Figure 1.2

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Data for Business Analytics

(continued)

Classifying Data Elements in a Purchasing Database

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Categorical

Categorical

Categorical

Ratio

Categorical

Ratio

Ratio

Ratio

Interval

Interval

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Modifying Data in Excel�Sorting Data in Excel

• Step 1. Select cells A1:F21
• Step 2. Click the Data tab in the Ribbon
• Step 3. Click Sort in the Sort & Filter group
• Step 4. Select the check box for My data has headers
• Step 5. In the first Sort by dropdown menu, select Sales (March 2010)
• Step 6. In the Order dropdown menu, select Largest to Smallest (see Figure 2.4)
• Step 7. Click OK

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• Ref book pg 24

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Filtering

• Step 1. Select cells A1:F21
• Step 2. Click the Data tab in the Ribbon
• Step 3. Click Filter in the Sort & Filter group
• Step 4. Click on the Filter Arrow in column B, next to Manufacturer
• Step 5. If all choices are checked, you can easily deselect all choices by unchecking
• (Select All). Then select only the check box for Toyota.
• Step 6. Click OK

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Creating Distributions from Data

• Distributions help summarize many characteristics of a data set by describing how often certain values for a variable appear in that data set.
• Distributions can be created for both categorical and quantitative data, and they assist the analyst in determining variation.

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Frequency Distributions for Categorical Data

• A frequency distribution is a summary of data that shows the number (frequency) of observations in each of several non overlapping classes, typically referred to as bins.

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Frequency Distribution

Frequency Distribution of Age

Grouped Frequency Distribution of Age:

Consider a data set of 26 children of ages 1-6 years. Then the frequency distribution of variable ‘age’ can be tabulated as follows:

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Example: 1

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A survey was taken in Maple Avenue. In each of 20 homes, people were asked how many cars were registered to their households. The results were recorded as follows:

3, 1, 4, 0, 2, 1, 5, 2, 1, 5, 4, 2, 3, 2, 0, 2, 1, 0, 3, 2.

Present this data in Frequency Distribution Table.

Also find maximum number of cars registered by household.

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Example: 2

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Solution ?

• Discussed in class

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Relative Frequency and Percent Frequency Distributions

• A relative frequency distribution is a tabular summary of data showing the relative frequency for each bin.

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• A percent frequency distribution summarizes the percent frequency of the data for each bin.

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Relative Frequency and Percent Frequency Distributions

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for Coca-Cola is 19/50 = 0.38,

for Diet- Coke is 8/50 = 0.16, and so on.

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Example: 3

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Frequency Distributions for Quantitative Data

• Consider the quantitative data in Table 2.6

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• These data show the time in days required to complete year-end audits for a sample of 20 clients of Sanderson and Clifford, a small public accounting firm. The three steps necessary to define the classes for a frequency distribution with quantitative data are as follows:

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1. Determine the number of non overlapping bins.
2. Determine the width of each bin.
3. Determine the bin limits.

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• Number of Bins: Bins are formed by specifying the ranges used to group the data.
• Width of the Bins: choose a width for the bins.

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bin width of (33 -12)/5 = 4.2 Approx. is 5

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• Bin Limits: Bin limits must be chosen so that each data item belongs to one and only one class.

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lower and upper bin limits to obtain a total of five classes:

10–14,

15–19,

20–24,

25–29,

30–34.

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Example: 4

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• Step 1. Select cells B10:B14
• Step 2. Type the formula 5FREQUENCY(A2:D6, A10:A14). The range A2:D6
• defines the data set, and the range A10:A14 defines the bins.
• Step 3. Press CTRL+SHIFT1+ENTER after typing the formula in Step 2.

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Data Presentation

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Two types of statistical presentation of data - graphical and numerical.

Graphical Presentation: We look for the overall pattern and for striking deviations from that pattern. Over all pattern usually described by shape, center, and spread of the data. An individual value that falls outside the overall pattern is called an outlier.

Bar diagram and Pie charts are used for categorical variables.

Histogram, stem and leaf and Box-plot are used for numerical variable.

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Histograms

• Step 1. Click the Data tab in the Ribbon
• Step 2. Click Data Analysis in the Analyze group
• Step 3. When the Data Analysis dialog box opens, choose Histogram from the list of
• Analysis Tools, and click OK
• In the Input Range: box, enter A2:D6
• In the Bin Range: box, enter A10:A14
• Under Output Options:, select New Worksheet Ply:
• Select the check box for Chart Output (see Figure 2.13)
• Click OK

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A common graphical presentation of quantitative data is a histogram

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Thank You !

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