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Introduction to Statistics: Help and Review9 chapters | 137 lessons

Instructor:
*Beverly Maitland-Frett*

Beverly has taught mathematics at the high school level and has a doctorate in teaching and learning.

Intentionally or unintentionally, we reason deductively. In this lesson, we will examine the definition of deductive arguments, look at some uses and explore some examples of ways in which we reason or argue deductively.

Everyday we reason deductively. This just means that we use facts that we already know to build on other facts until we come to a desired conclusion. For example, Sully spent some time in a major mall. Now it's time for her to go home, but she forgot where she parked her car. She knows that her car is blue, fact number 1. She also knows that her make is Honda, fact number 2. She remember that she parked between section E and D. So, what can she do? Of course, she is going to check all the blue Hondas in section E until she identifies her car. That is what deductive reasoning is about. You use your general knowledge about something to arrive at a specific conclusion.

An argument begins with a statement that we believe to be true or false, which we call the premise. Then we reason in a logical manner to arrive at a conclusion. A **deductive argument** is a type of logical argument that begins with a factual premise such that the conclusion you want to reach must be true. It uses deductive reasoning to arrive at a conclusion. Sully used the general factual premise that she drives a blue Honda to search for her specific car. Had she started searching for a red Honda, she would have never found her car. She began with facts about her car and, ultimately, will have to find her car. Therefore, a deductive argument begins with a known fact that will ultimately lead to conclusion that is true. Remember, with deductive reasoning, you will undoubtedly arrive at a true conclusion. If you don't, then you didn't begin with a factual statement.

Deductive arguments are used mainly in mathematics, sciences, and philosophical debates. In mathematics, deductive arguments are used to derive mathematical theorems and formulas, and in geometrical proofs. In sciences, these arguments help to make conclusions about human, plant and animal development, as well as the prevention and cure of diseases. Plus, as mentioned earlier, we constantly use deductive reasoning without knowing it.

We will explore some mathematical arguments.

Example 1: Use deductive reasoning to prove that a quadrilateral is a polygon.

A polygon is a closed figure having three or more sides. This is the general factual premise that we will start with. Another fact we know is that a quadrilateral is a four-sided closed figure. Since a quadrilateral is a four-sided closed figure, and four is more than three, then a quadrilateral must be a polygon.

Example 2: Let's examine a two column geometric proof.

In this example, we began with the general premise that figure ROMP is a square. Now, we have to use that knowledge to prove that the diagonals RM and OP are congruent. Therefore, we showed that the sides are congruent by definition of a square, another fact. Then we proved that two shapes that have congruent sides are congruent, proving two congruent triangles. If the triangles are congruent, then their corresponding sides are congruent, making the diagonals congruent. We moved from the general case of a square to the specific case of square ROMP.

Example 3: Here is a simple scientific proof. Show that dolphins are mammals.

A mammal is a warm-blooded animal, that gives suck to its young. This is the general case. Since dolphins give suck to their young and are warm-blooded, we can conclude that dolphins are mammals.

Example 4: Marcy took her umbrella to work today, and she did not get wet. Show that it rained today.

Firstly we know that Marcy took her umbrella. However, that doesn't prove that it was raining. It could be sunny and she didn't want to get a sunburn, which also explains why she didn't get wet. Nothing here helps us proved that it rained; therefore, we cannot use deductive reasoning.

Deductive argument uses factual statements to arrive at other factual statements, which leads to a true conclusion. It builds from a general factual premise to arrive at a specific conclusion. Deductive arguments have helped mathematicians, scientist and philosophers make important conclusions about life. In mathematics, deductive arguments are used to solve geometric proofs.

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Introduction to Statistics: Help and Review9 chapters | 137 lessons

- Descriptive & Inferential Statistics: Definition, Differences & Examples 5:11
- Difference between Populations & Samples in Statistics 3:24
- Defining the Difference between Parameters & Statistics 5:18
- Estimating a Parameter from Sample Data: Process & Examples 7:46
- What is Quantitative Data? - Definition & Examples 4:11
- What is Categorical Data? - Definition & Examples 5:25
- Discrete & Continuous Data: Definition & Examples 3:32
- Nominal, Ordinal, Interval & Ratio Measurements: Definition & Examples 8:29
- The Purpose of Statistical Models 10:20
- Experiments vs Observational Studies: Definition, Differences & Examples 6:21
- Random Selection & Random Allocation: Differences, Benefits & Examples 6:13
- Convenience Sampling in Statistics: Definition & Limitations 6:27
- How Randomized Experiments Are Designed 8:21
- Analyzing & Interpreting the Results of Randomized Experiments 4:46
- Confounding & Bias in Statistics: Definition & Examples 3:59
- Bias in Polls & Surveys: Definition, Common Sources & Examples 4:36
- Misleading Uses of Statistics 8:14
- Causation in Statistics: Definition & Examples 3:28
- Deductive Argument: Definition & Examples
- Observational Study in Statistics: Definition & Examples 5:55
- Skewness in Statistics: Definition, Formula & Example 6:49
- Uniform Distribution in Statistics: Definition & Examples 4:58
- Confidence Interval: Definition, Formula & Example 7:33
- Chi Square Distribution: Definition & Examples 4:55
- Chi Square Practice Problems 6:53
- Chi Square: Definition & Analysis 4:04
- How to Calculate a Chi Square: Formula & Example 4:13
- Go to Overview of Statistics: Help and Review

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