Is a characteristic that has two or more mutually exclusive values or properties?

Lesson 2: Summarizing Data

Section 2: Types of Variables

Look again at the variables (columns) and values (individual entries in each column) in Table 2.1. If you were asked to summarize these data, how would you do it?

First, notice that for certain variables, the values are numeric; for others, the values are descriptive. The type of values influence the way in which the variables can be summarized. Variables can be classified into one of four types, depending on the type of scale used to characterize their values (Table 2.2).

Table 2.2 Types of Variables

Scale	Example	Values
Nominal Ordinal “categorical” or “qualitative”	disease status ovarian cancer	yes / no Stage I, II, III, or IV
Interval Ratio “continuous” or “quantitative”	date of birth tuberculin skin test	any date from recorded time to current 0 – ??? of induration

• A nominal-scale variable is one whose values are categories without any numerical ranking, such as county of residence. In epidemiology, nominal variables with only two categories are very common: alive or dead, ill or well, vaccinated or unvaccinated, or did or did not eat the potato salad. A nominal variable with two mutually exclusive categories is sometimes called a dichotomous variable.
• An ordinal-scale variable has values that can be ranked but are not necessarily evenly spaced, such as stage of cancer (see Table 2.3).
• An interval-scale variable is measured on a scale of equally spaced units, but without a true zero point, such as date of birth.
• A ratio-scale variable is an interval variable with a true zero point, such as height in centimeters or duration of illness.

Nominal- and ordinal-scale variables are considered qualitative or categorical variables, whereas interval- and ratio-scale variables are considered quantitative or continuous variables. Sometimes the same variable can be measured using both a nominal scale and a ratio scale. For example, the tuberculin skin tests of a group of persons potentially exposed to a co-worker with tuberculosis can be measured as “positive” or “negative” (nominal scale) or in millimeters of induration (ratio scale).

Table 2.3 Example of Ordinal-Scale Variable: Stages of Breast Cancer*

* This table describes the stages of breast cancer. Note that each stage is more extensive than the previous one and generally carries a less favorable prognosis, but you cannot say that the difference between Stages 1 and 3 is the same as the difference between Stages 2 and 4.

Exercise 2.1

For each of the variables listed below from the line listing in Table 2.1, identify what type of variable it is.

1. Nominal
2. Ordinal
3. Interval
4. Ratio

1. ____ Date of diagnosis
2. ____ Town of residence
3. ____ Age (years)
4. ____ Sex
5. ____ Highest alanine aminotransferase (ALT)

Check your answer.

What Is Mutually Exclusive?

Mutually exclusive is a statistical term describing two or more events that cannot happen simultaneously. It is commonly used to describe a situation where the occurrence of one outcome supersedes the other. For example, war and peace cannot coexist at the same time. This makes them mutually exclusive.

Key Takeaways

• Events are considered to be mutually exclusive when they cannot happen at the same time.
• The concept often comes up in the business world in the assessment of budgeting and dealmaking.
• If considering mutually exclusive options, a company must weigh the opportunity cost, or what it would be giving up by choosing each option.
• The time value of money (TVM) is often considered when deciding between two mutually exclusive choices.
• Not mutually exclusive means that two instances or outcomes can occur simultaneously, and one outcome does not limit the other from being possible.

Understanding Mutually Exclusive

Mutually exclusive events are events that can't both happen, but should not be considered independent events. Independent events have no impact on the viability of other options. For a basic example, consider the rolling of dice. You cannot roll both a five and a three simultaneously on a single die. However, you absolutely can roll a five and a three on two dice. Rolling a five and three simultaneously means this outcome is mutually exclusive. Rolling a five on one and a three on the other means they are not mutually exclusive outcomes.

Opportunity Cost

When faced with a choice between mutually exclusive options, a company must consider the opportunity cost, which is what the company would be giving up to pursue each option. The concepts of opportunity cost and mutual exclusivity are inherently linked because each mutually exclusive option requires the sacrifice of whatever profits could have been generated by choosing the alternate option.

The time value of money (TVM) and other factors make mutually exclusive analysis a bit more complicated. For a more comprehensive comparison, companies use the net present value (NPV) and internal rate of return (IRR) formulas to mathematically determine which project is most beneficial when choosing between two or more mutually exclusive options.

Example of Mutually Exclusive

The concept of mutual exclusivity is often applied in capital budgeting. Companies may have to choose between multiple projects that will add value to the company upon completion. Some of these projects are mutually exclusive.

For example, assume a company has a budget of $50,000 for expansion projects. If available Projects A and B each cost $40,000 and Project C costs only $10,000, then Projects A and B are mutually exclusive. If the company pursues A, it cannot also afford to pursue B and vice versa. Project C may be considered independent. Regardless of which other project is pursued, the company can still afford to pursue C as well. The acceptance of either A or B does not impact the viability of C, and the acceptance of C does not impact the viability of either of the other projects.

Moreover, when looking at opportunity costs, consider the analysis of Projects A and B. Assume that Project A has a potential return of $100,000, while Project B will only return $80,000. Since A and B are mutually exclusive, the opportunity cost of choosing B is equal to the profit of the most lucrative option (in this case, A) minus the profits generated by the selected option (B); that is, $100,000 - $80,000 = $20,000. Because option A is the most lucrative option, the opportunity cost of going for option A is $0.

What Does It Mean If Projects Are Mutually Exclusive?

In business, managers and directors often need to plan resource allocation. If a company is building a bridge and a skyscraper, and both projects require an extremely specialized piece of equipment and only one exists in the world, it would mean that these projects are mutually exclusive, as that piece of equipment cannot be used by both projects at the same time. This idea can be extended to consider specialized professionals, software systems (which cannot run both Mac and Windows), and allocated budgets.

What Is the Difference Between Independent and Mutually Exclusive?

To illustrate the difference between what is independent and what is mutually exclusive, consider the war and peace example from earlier. There could be war in France and peace in Italy. These are two independent nations and therefore each one could be in its own state of peace. However, there cannot be war in France and peace in France. Since they cannot coexist, that makes them mutually exclusive.

What Does Mutually Exclusive Mean in Finance?

Typically, this involves budgeting and payments. If a company has $180 million to spend, it cannot spend that $180 million both by reinvesting in the business and offering bonuses to upper management. In this case, those two options are mutually exclusive. If the company can only retain licensing in a single country, that means they should not attempt to be licensed in two separate countries as they are mutually exclusive.

The Bottom Line

Things that are mutually exclusive are not able to occur simultaneously. In business, this is typically concerning the undertaking of projects or allocating a budget. If two things are not mutually exclusive, it means the existence and occurrence of one does not necessarily mean the other cannot coexist.

What refers to the characteristics that have two or more mutually exclusive values or properties?

Is a characteristic that takes two or more values which varies across individual?

What is a variable characteristic?

What are the characteristics of independent variable?