Quantitative Methods Online Course Notes

• Welcome to the pre-assessment test for the HBS Quantitative Methods Tutorial.
• All questions must be answered for your exam to be scored.
• After submitting your answer, you will not be able to change it.
• You may skip a question, but all questions must be answered for the exam to be scored.
• Links to Excel spreadsheets containing z-value and t-value tables are provided.
• Your results will be displayed immediately upon completion of the exam.
• After completion, you can review your answers at any time by returning to the exam.
• The exam questions have a level of difficulty similar to the exercises in the course.
• Yes, This is an open-book examination.
• No, you may neither give nor receive help on any exam question.
• No, This is not a timed exam, you should take about 60-90 minutes to complete the exam.
• Your answer choices will be recorded and you will be able to pick up where you left off when you return to the exam site.
• Your results will be displayed as soon as you submit your answer to the final question.

Overview & Introduction

• This course will help you develop your skills and instincts in applying quantitative methods to formulate, analyze, and solve management decision-making problems.
• QM is designed to help you develop quantitative analysis skills in business contexts.
• Mastering its content will help you evaluate management situations you will face not only in your studies but also as a manager.
• QM won't make you a statistician, but it will help you become a more effective manager.
• The tutorial's primary emphasis is on developing good judgment in analyzing management problems.
• Whether you are learning the material for the first time or are using QM to refresh your quantitative skills, you can expect the tutorial to improve your ability to formulate, analyze, and solve managerial problems.
• QM's interactive nature provides frequent opportunities to assess your understanding of the concepts and how to apply them in the context of actual management problems.
• You should take 15 to 20 hours to run through the whole tutorial, depending on your familiarity with the material.
• QM offers many features that you will explore, utilize, and enjoy.

The Story and its Characters

• You're flying out to Hawaii after all, staying at a 5-star hotel as a Summer Associate with Avio Consulting.
• You are excited that the firm has assigned Alice, one of its rising stars, as your mentor.
• It seems clear that Avio partners consider you a high potential intern — they are willing to invest in you with the hope that you will later return after you complete your MBA program.
• Alice recently received the latest in a series of quick promotions at Avio.
• This is her first assignment as a project lead: providing consulting assistance to the Kahana, an exclusive resort hotel on the Hawaiian island Kauai.
• Leo inherited the Kahana just three years ago and has asked for Avio's help to bring a more rigorous approach to his management decision-making process.

Using the Tutorial: A Guide to Tutorial Resources

• QM's structure and navigational tools are easy to master.
• There are three types of interactive clips: Kahana Clips, Explanatory Clips, and Exercise Clips.

Kahana Clips

• Kahana Clips pose problems that arise in the context of your consulting engagement at the Kahana.
• You will analyze the problem, and you and Alice will present your results to Leo for his consideration.
• The Kahana Clips will give you exposure to the types of business problems that benefit from the analytical methods you'll be learning, and a context for practicing the methods and interpreting their results.
• You should solve all of Leo's problems.
• At the end of the tutorial, a multiple-choice assessment exam will evaluate your understanding of the material.

Explanatory Clips

• In Explanatory Clips, you will learn everything needed to analyze management problems like Leo's.
• Complementing the text are graphs, illustrations, and animations that will help you understand the material, you'll be asked questions to check your understanding of the concepts.
• Some Explanatory Clips give you directions or tips on how to use the analytical and computational features of Microsoft Excel.
• Facility with the necessary Excel functions will be critical to solving the management decision problems in this course.
• QM is supplemented with spreadsheets of data relating to the examples and problems presented.

Exercise Clips

• Exercise Clips provide additional opportunities for you to test your understanding of the material.
• Work through exercises to solidify your knowledge of the material.
• Challenge exercises provide opportunities to tackle somewhat more advanced problems.
• The challenge exercises are optional - you should not have to complete them to gain the mastery needed to pass the tutorial assessment test.
• The arrow buttons immediately below are used for navigation within clips.
• In the upper right of the QM tutorial screen are three buttons that are links to the Help, Briefcase, and Glossary.
• In your Briefcase you'll find all the data you'll need to complete the course, neatly stored as Excel workbooks.
• In the Glossary/Index you'll find a list of helpful definitions of terms used in the course, along with brief descriptions of the Excel functions used in the course.
• Utilize all of QM's features and resources to the fullest and build an intuition for quantitative analysis that you will need as an effective and successful manager.

and Welcome to Hawaii!

• Leo sounds like he's the kind of manager who usually relies on gut instincts to make business decisions and likes to take risks.
• He's hired Avio to help him make managerial decisions with, well, better judgment.
• He wants to learn how to approach management problems in a more sophisticated, analytical fashion.
• You'll be using some basic statistical tools and methods to do quite a bit of the analytic work soon.

Leo and the Hotel Kahana

• Leo has been trying his best to run the Kahana the way a hotel of its quality deserves, but he has to get more serious about the way he makes decisions.
• He wants to approach management problems in a more sophisticated, analytical fashion using basic statistical tools and methods.

Basics: Data Description Leo's Data Mine

• Leo has assembled the most important data on the Kahana, and there's just so much to keep track of.
• There are two things, in particular, that have been on Leo's mind recently.

recreational activities

• We offer some recreational activities here at the Kahana, including a scuba diving certification course.
• I contract out the operations to a local diving school.
• The contract is up soon, and I need to renew it, hire another school, or discontinue offering scuba lessons all together.
• I'd like you to get me some quotes from other diving schools on the island so I get an idea of the competition's pricing and how it compares to the school I've been using.

hotel occupancy rates

• I'm very concerned about hotel occupancy rates.
• The Kahana's occupancy fluctuates during the year, and I'd like to know how, when, and why.
• I'd love to have a better feeling for how many guests I can expect in a given month.
• These files contain some information about tourism on the island, but I'd really like you to help me make better sense of it.
• Somehow I feel that if I could understand the patterns in the data, I could better predict my own occupancy rates.

What is Alice getting at when she tells you to "understand the data"? And how can you develop such an understanding?

• Data can be represented by graphs like histograms, and the data we encounter each day have valuable information buried within them.
• As managers, correctly analyzing financial, production, or marketing data can greatly improve the quality of the decisions we make.
• Analyzing data can be revealing, but challenging and we want to extract as much of the relevant information and insight as possible from the data we have available.

Important Questions To Ask About Data

• When we acquire a set of data, we should begin by asking these important questions: Where do the data come from? How were they collected? How can we help the data tell their story?
• Before starting any type of formal data analysis, we should try to get a preliminary sense of the data.
• For example, we might first try to detect any patterns, trends, or relationships that exist in the data.
• We might start by grouping the data into logical categories, and this can help us identify patterns within a single category or across different categories.

Accountants

• Accountants arrange information to make it easier to comprehend with Balance Sheets and Profit and Loss Statements.
• Accountants separate costs into categories such as capital investments, labor costs, and rent.
• We might ask: Are operating expenses increasing or decreasing? Do office space costs vary much from year to year?
• Comparing data across different years or different categories can give us further insight. Are selling costs growing more rapidly than sales? Which division has the highest inventory turns?

Histograms

• In addition to grouping data, we often graph them to better visualize any patterns in the data.
• Seeing data displayed graphically can significantly deepen our understanding of a data set and the situation it describes.
• A histogram shows us where the data tend to cluster. What are the most common values? The least common?

Outliers

• In many data sets, there are occasional values that fall far from the rest of the data known as outliers.
• First, we must investigate why an outlier exists. Is it just an unusual, but valid value? Could it be a data entry error? Was it collected in a different way than the rest of the data? At a different time?
• After making an effort to understand where an outlier comes from, we should have a deeper understanding of the situation the data represent.
• Typically, we do one of three things: leave the outlier alone, or very rarely remove it or change it to a corrected value.
• Excluding or changing data is not something we do often. We should never do it to help the data 'fit' a conclusion we want to draw.
• Such changes to a data set should be made on a case-by-case basis only after careful investigation of the situation.

Summary

• With any data set we encounter, we must find ways to allow the data to tell their story.
• Ordering and graphing data sets often expose patterns and trends, thus helping us to learn more about the data and the underlying situation.
• If data can provide insight into a situation, they can help us to make the right decisions.

Creating Histograms

• Create histograms with Excel involves two steps: preparing our data, and processing them with the Data Analysis Histogram tool.
• To prepare the data, we enter or copy the values into a single column in an Excel worksheet.
• Often, we have specific ranges in mind for classifying the data. We can enter these ranges, which Excel calls "bins," into a second column of data.
• In the Tool bar, select the Data tab, and then choose Data Analysis. In the Data Analysis pop-up window, choose Histogram and click OK.
• Click on the Input Range field and enter the range of data values by either typing the range or by dragging the cursor over the range.
• Note: if we don't specify our own bins, Excel will create its own bins, which are often quite peculiar.
• Click the Chart Output checkbox to indicate that we want a histogram chart to be generated in addition to the summary table, which is created by default.
• Click New Worksheet Ply, and enter the name you would like to give the output sheet. Finally, click OK, and the histogram with the summary table will be created in a new sheet.

Central Values for Data

• Graphs are very useful for gaining insight into data. However, sometimes we would like to summarize the data in a concise way with a single number.

The Mean

• We'd like that summary value to describe the data as well as possible.
• The numerical average would probably work quite well as a single value representing employees' experiences.
• To calculate average — or mean — employee satisfaction, we take all the scores, sum them up, and divide the result by the number of surveys.
• The Greek letter mu represents the mean of the data set, that is by far the most common measure used to describe the "center" or "central tendency" of a data set.
• However, it isn't always the best value to represent data: Outliers can exercise undue influence and pull the mean value towards one extreme; in addition, if the distribution has a tail that extends out to one side — a skewed distribution — the values on that side will pull the mean towards them.

The Median

• In cases like income, where the data are typically very skewed, the mean often isn't the best value to represent the data.
• In these cases, we can use another central value called the median, which is the middle value of a data set whose values are arranged in numerical order.
• Half the values are higher than the median, and half are lower.
• Median revenue is a more informative revenue estimate because it is not pulled upwards by a small number of high- revenue earners.
• With an odd number of data points, listed in order, the median is simply the middle value; in a data set with an even number of points, we average the two middle values.
• When deciding whether to use a mean or median to represent the central tendency of our data, we should weigh the pros and cons of each.
• The mean weighs the value of every data point, but is sometimes biased by outliers or by a highly skewed distribution. By contrast, the median is not biased by outliers and is often a better value to represent skewed data.

The Mode

• A third statistic to represent the "center" of a data set is its mode: the data set's most frequently occurring value.
• We might use the mode to represent data when knowing the average value isn't as important as knowing the most common value.
• In some cases, data may cluster around two or more points that occur especially frequently, giving the histogram more than one peak: bi-modal distribution is a distribution that has two peaks.

Summary

• To summarize a data set using a single value, we can choose one of three values: the mean, the median, or the mode. They are often called summary statistics or descriptive statistics.
• All three give a sense of the "center" or "central tendency" of the data set, but we need to understand how they differ before using them:

Finding The Mean In Excel

• To find the mean of a data set entered in Excel, we use the AVERAGE function.
• We can find the mean of numerical values by entering the values in the AVERAGE function, separated by commas.
• In most cases, it's easier to calculate a mean for a data set by indicating the range of cell references where the data are located.
• Excel ignores blank values in cells, but not zeros.
• Therefore, we must be careful not to put a zero in the data set if it does not represent an actual data point.

Finding The Median In Excel

• Excel can find the median, even if a data set is unordered, using the MEDIAN function.
• The easiest way to calculate a data set's median is to select a range of cell references.

Finding The Mode In Excel

• Excel can also find the most common value of a data set, the mode, using the MODE function.
• If more than one mode exists in a data set, Excel will find the one that occurs first in the data.

Variability

- The mean, median and mode give you a sense of the center of the data, but none of these indicate how far the data are spread around the center.