25 Oct In both for-profit and not-for-profit organizations, statistics are critical pieces of information that allow decision makers to steer the organization in directions that are in the
In both for-profit and not-for-profit organizations, statistics are critical pieces of information that allow decision makers to steer the organization in directions that are in the organization's best interest. Data is acquired from many sources, some within the organization, and some from outside the organization. The government tracks data on many different aspects of society (including industrial output). The following will guide your thinking about the uses of data and information.
Review the important themes within the sub question of each bullet point. The sub questions are designed to get you thinking about some of the important issues. Your response should provide a succinct synthesis of the key themes in a way that articulates a clear point, position, or conclusion supported by research.
You are analyzing the cross-store sales of a grocery store chain. As part of your analysis, you compute two measures of central tendency—mean and median. The mean sales are $358.4 million, and the median sales are $163.1 million (per store).
- To quantify the average sales per store, evaluate which of the two measures would you use and why. Support your discussion with relevant examples, research, and rationale.
The final paragraph (three or four sentences) of your initial post should summarize the one or two key points that you are making in your initial response.
Submission Details
- Your posting should be the equivalent of 1 to 2 single-spaced pages (500–1000 words) in length.
- Since you are engaging in research, be sure to cite in the body of the post and add a reference list in APA format
- Comment on 2 student responses attached
Probability.html
Probability
Uncertainty is a threat in business because it puts scarce resources at risk. Accordingly, a considerable amount of effort is put into diminishing uncertainty across all aspects of business operations.
One of the best tools available to business managers to quantify the risk associated with the unknown is probability theory. Probability theory offers a means of reducing uncertainty by estimating the chances of different outcomes occurring. For example, knowing that in a particular process, Outcome A has a 5 percent chance of materializing while Outcome B has a 95 percent chance of materializing will greatly reduce the uncertainty associated with the outcome that can be expected from this process. However, uncertainty can rarely be eliminated altogether.
Analysis using probabilities for Outcome A and Outcome B can be achieved through the use of decision trees. Organizations simply represent each possible outcome of a situation, the likelihood that each outcome will occur (5% for Outcome A and 95% for Outcome B), and the monetary value associated with each outcome. Then, based on those probabilities, the organization can decide which alternative to choose, based on which outcome gives the likelihood of the highest profit.
Probability estimation can be based on prior knowledge of the process involved, for example, the roll of a die, or on an analysis of past events such as the frequency with which an event occurred. Alternatively, probability estimation can be based on qualitative considerations, such as a survey of expert opinion. Probabilities based on known processes are known as classical probabilities. Those based on an analysis of recurring events are known as frequentist probabilities. The subjective estimation of probabilities is known as Bayesian probability (named after its inventor, Thomas Bayes). This course focuses on classical and frequentist approaches. Qualitative approaches (like Bayesian probability) are available for further study.
An example of probability based on known events is the probabilities associated with the throw of a die. In a business context, instances of known probabilities associated with a process are rare. However, frequentist probability determinations are common. Examples include frequency of product returns, the proportion of defective parts in a shipment, the length of time of telephone calls, and so on. Bayesian probabilities are used to estimate the probabilities of particular customers placing orders, the rate of output of a research program, or the risks associated with political or economic changes. Again, as Bayesian approaches address circumstances that are rare, unusual, and/or difficult to quantify, they will not be treated in this course.
A typical business application of probability theory might address, for example, the question of preferences for regular or decaffeinated coffee. To do this a survey is carried out at a selected coffee shop. Of 200 respondents, 125 are male and 75 are female. 120 prefer regular coffee and 80 prefer decaffeinated coffee. Of the males, only 45 prefer decaffeinated coffee.
Using a frequentist approach to estimating probabilities, it is apparent from this data that the percentage of people who prefer regular coffee can be estimated at 120/200 or 60%. The percentage of males who prefer decaffeinated coffee is given as 45/125 or 36%. The percentage of females who prefer decaffeinated coffee is, therefore, 35/75 or approximately 47%.
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Measures of Central Tendency.html
Measures of Central Tendency
Summary data are generally communicated by representative measures. The "typical" age of a student in an MBA class might be represented by the average age of the students in the MBA class. The entire collection of all possible observations (in this case, all of the students in the MBA class) represents the population in which the statistician is interested. When a single measure is used, it generally represents the most common measurement of the population statistic. For this reason, such measures are commonly termed measures of central tendency, because they represent the measure that is more or less in the middle of the observations. Common measures of central tendency are the mean (also known as the simple average), the median, and the mode.
Measures of central tendency can vary in their appropriateness as a measure of central tendency. For example, the mean age of participants in a Boy Scouts camping trip may be 21, but that may not be a realistic reflection of the age of any of the participants in the trip (which might include young boys and older Scout leaders, but might not include any young adults that might be suggested by the calculated mean value of age). Thus, appropriate judgment must be exercised in deciding which measure of central tendency is appropriate in a given situation.
Most of the time, organizations choose between mean and median as the appropriate measure of central tendency. If a measure is expected to take all data into consideration, then the mean is likely the appropriate measure to consider. However, if an organization is looking for a “typical” value for a variable, then the median may be the more appropriate choice.
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Measures of Variability.html
Measures of Variability
Often, to gain better insights into the nature of a population, it is desirable to describe the population by more than its measure of central tendency. One may question, as discussed in the previous video, how good a representation of the population the mean (or average) really is. To answer this question, measures of variability are used in conjunction with measures of central tendency to more fully describe the data. For example, a measure of the mean (a measure of central tendency) of a population may be augmented by information about the range of observations (a measure of variability of the population, which is calculated by subtracting the smallest value of a population from the largest value). Knowing the ages of the youngest and oldest participants in the camping trip discussed in the previous video provides us with more information than simply knowing the mean age of all participants.
Two other measures of variability are the variance of the population and the standard deviation of the population. There is a relationship between these two measures of variability, as the standard deviation squared (multiplied by itself) is the variance. Looking at it another way, standard deviation is the square root of the variance.
The units of measurement of the standard deviation make it more useful than the variance in some circumstances. For example, if the measure of central tendency that we are considering is measured in dollars, then standard deviation will also be in dollars. Variance would be in units of “dollars squared,” which is not something that is easy for us to comprehend, in terms of exactly what that means.
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Descriptive vs. Inferential Statistics.html
Descriptive vs. Inferential Statistics
Descriptive statistics are used to describe the characteristics that can be known about a collection of data. Inferential statistics, on the other hand, are generalizations that we are able to make about a larger collection of data (known as a population) from the smaller collection of data that we collected (referred to as a sample).
In statistics, we are interested in collecting the values for certain characteristics about the subjects that we are studying. For example, the characteristics that we might collect from a patient in a doctor’s office would be height, weight, and blood pressure. Each of these values is a characteristic, and we refer to each of these characteristics as variables.
To understand the different types of variables, we need to start with the basic question, what are data? Let's begin by learning about data and the different types of data.
In business, data are simply facts. There are different types of facts, such as about purchases that have been made, outcomes that have materialized, or events that have been observed. There is an infinite variety of facts; yet, in terms of how these facts are recorded (that is, made into what we call data), there are four basic, mutually exclusive types of data groupings: nominal, ordinal, interval, and ratio. These types of data capture how individual facts are encoded, rather than their intrinsic meaning. For instance, the term "hundred" might be a nominal measure if it refers to the observation being part of a group named hundred, or it might be an interval scale measure as in the number 100.
In theory, a given variable can be measured on any of the aforementioned four scales. However, in practice, some variables presuppose a particular scale. For instance, variables that are used to label states or phenomena, such as gender, are usually measured using nominal scales, while measures that connote ordering or ranking, such as finishing position in a race (first, second, third, etc.), are measured using ordinal scales.
See the Supplemental Media entitled “Variable Classification” for more information about how data is classified.
Additional Materials
Variable Classification Qualitative or Quantitative?
media/transcripts/SUO_MBA5008 W1 L1 Variable Classification.pdf
Variable Classification Qualitative or Quantitative?
Interval data are those data values that reflect a difference between two observations, with the difference having meaning. For example, if the temperature yesterday was 80°F, and the temperature today is 60°F, then the change in temperature has been a decrease of 20°F. This difference between the two observations represents an interval. The same interval would exist if the temperature change in a 24 hour period was from 40°F to 20°F. We know what the interval means, as we have an awareness of what 20°F means.
A datum (a specific piece of data) can have a special meaning that would cause it to be considered a ratio variable. A ratio variable is a special form of data value that has a specific meaning for the value of zero that will cause measurements relative to that zero value to carry a specific meaning. For example, if the amount of milk in a recipe is zero, then there is none of that ingredient in the dish that you are preparing. If another dish called for two tablespoons of milk, then that would mean that the second dish has twice as much milk in it as a third dish that called for only one tablespoon of milk. Thus, the relative values (ratios) of milk in the second and third dishes have meaning (the second dish has twice as much milk as the third dish, since 2/1 = 2) relative to the value of zero. The same thing cannot be said about the interval data (like temperatures) discussed in the previous paragraph, as the pairs of values discussed there cannot be compared to zero in the same way (40°F is not twice as hot as 20°F).
From a practical standpoint, the four data measurement types are usually collapsed into two broad categories—qualitative and quantitative. Qualitative data, also referred to as categorical data, encompasses nominal and ordinal measures distinguished by their nature or quality rather than their numerical value in measurement. Quantitative data, also referred to as continuous data, combines interval and ratio measures typically measured using numerical values. The rationale for using quantitative and qualitative data types is driven as much by convenience as by the nature of commonly used business data. It is easier to think of data in terms of two, rather than four, data types.
In addition to the above general types of variables, business analysts also distinguish between original or source data and summary metrics, particularly in situations where data is voluminous. For instance, consider the universal product code (UPC) scanner data (the point-of-sale data collected with the help of scanning devices). At a large grocery or mass merchandise outlet, a single day will result in thousands, or even millions, of individual data points; however, it matters little whether a particular product was sold at 1:35 p.m. or 3:05 p.m. Therefore, the original or source data are frequently summarized with some relevant statistic, like the total number of units of the product sold during the day, being reported.
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