Introduction to Statistics

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Introductory Statistics as Covered in the Social, Behavioral, and Natural Sciences

679 students enrolled

What Will I Learn?

- Understand and learn how to calculate a number of different descriptive statistics
- Increase your quantitative and numerical reasoning skills!
- Increase marketable job skills in data analytics

Requirements

- No special software or other materials are required.

Description

**June, 2017:**

In the course, you will learn how to easily and effectively analyze and interpret data involving introductory statistics. The following topics are covered in this course:

**Scales of measurement** - nominal, ordinal, interval, ratio.

: Easily understand the often-confused scales of measurement covered in most statistics texts.*Goal/Learning Objective*

**Central Tendency** - mean, median, and mode are illustrated along with practice problems; measures of central tendency and skewed distributions are explained, as well as how to calculate the weighted mean.

Summarize a set of data, find the center location in a distribution of scores, understand and identify the location of measures of central tendency in skewed distributions, understand and interpret how to find the overall or combined mean for two different sets of data.*Goals/Learning Objectives*:

**Variability** - How to calculate the standard deviation and variance as well as how to interpret percentiles are provided in simple and clear language.

Understand and explain variability (spread) in a set of numbers, including how to rank data and interpret data such as standardized test scores (for example, the 95th percentile).**Goals/Learning Objectives**:

**Charts and Graphs** - How to calculate a cumulative frequency distribution table as well as how to calculate a stem and leaf plot is illustrated.

Learn how to easily organize, summarize, understand, and explain a set of numbers.*Goals/Learning Objectives*:

**Probability, the Normal Curve and z-Scores** - An introduction to probability is provided, along with properties of the normal distribution and how to calculate and interpret z-scores

Understand beginning probability including important characteristics of the normal (Gaussian) distribution, as well as how to calculate and interpret z-scores.*Goals/Learning Objectives:*

** Bonus Features:** Cement understanding with practice opportunities including several quizzes with complete video coverage of the solutions.

**Update: New Videos Added on Hypothesis Testing! ****(See Section 6 of the Course.)**

Who is the target audience?

- Those interested in learning more about descriptive statistics should take this course (those interested only in inferential statistics should not take the course)

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Curriculum For This Course

30 Lectures

02:20:21
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Course Introduction and Introduction to Statistics
2 Lectures
13:43

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Central Tendency
6 Lectures
21:14

This video lecture covers the mean, median, and mode. First the mode is covered, including examples of two modes (bimodal) and three or more modes (multimodal). Next, finding the median is covered for both an even and odd number of values. After the median, how to calculate the mean (arithmetic average) is covered.

Mean, Median, and Mode (Measures of Central Tendency)

05:46

Quiz - Mean, Median, and Mode

5 questions

In this video, the answers to the mean, median, and mode quiz are reviewed with explanations provided. The answers are also available in the attached PDF file.

Note: On problem #5, I state, "1, 3, 3, 5", but should have stated "1, 3, 3, 3, 5."

Video Review of Quiz - Mean, Median, and Mode

04:12

In this video, we take a look at the relationship between the mean, median, and mode and asymmetrical (skewed) distributions. As the video illustrates, the order of the three measures of central tendency (where they fall on a number line in relation to each other) depends on whether a distribution is positively or negatively skewed.

Central Tendency and Skewed Distributions

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Quiz - Central Tendency and Skewed Distributions

3 questions

This video reviews the answers to the quiz on central tendency and skewed distributions. The answers are also available in the attached PDF file.

Video Review of Quiz - Central Tendency and Skewed Distributions

02:44

In this video, we take a look at the weighted mean, which can be used for finding an overall mean for two groups.

The Weighted Mean

04:42

The Weighted Mean

3 questions

In this video, the quiz answers are reviewed on the weighted mean.

Video Review of Quiz - The Weighted Mean

03:50

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Variability
3 Lectures
19:35

In this video, we take a look at percentiles, including quartiles and deciles.

Percentiles

05:55

Percentiles

5 questions

In this video, we take a look at how to calculate the variance and standard deviation by hand. Each step and calculation is illustrated in arriving at the solutions.

Calculating the Standard Deviation and Variance – Step by Step

06:29

Consider the following population of *N* = 5 values: X = 14, 9, 11, 7, 9. The population variance is equal to

Quiz - Standard Deviation and Variance

2 questions

This video reviews the quiz on the standard deviation and variance, illustrating step by step how to find each value.

Video Review of Quiz - Standard Deviation and Variance

07:11

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Charts, Tables, and Graphs
2 Lectures
06:00

In this video, we examine how to construct a cumulative frequency distribution table, which includes the columns X, f, and cf. X corresponds to the values (or scores) of a variable X, f is the frequency value for each X (how many of each X there are), and cf is the cumulative frequency.

- Goal: The purpose of creating this table is to organize (or provide order) to a set of numbers, which is one of the goals of statistics. After the table is created, notice how the largest and smallest values can be quickly and easily noted, as well as the modal (mode) value in the data set. Therefore, this table provides 'order' to the values.

How to Create a Cumulative Frequency Distribution Table

02:46

In this video we examine how to construct a stem and leaf plot on a set of numbers ranging from the tens to fifties.

- Goal: Like the frequency distribution table, the purpose of creating this table is to organize (or provide order) to a set of numbers, which is one of the goals of statistics. After the table is created, notice how the largest and smallest values can be noted fairly easily, as well as the modal (mode) value in the data set. Therefore, this table also provides 'order' to the values. As noted in the video, stem and leaf plots offer the added benefit of providing a plot of the distribution of values (if viewed from the side).

How to Create Stem and Leaf Plot

03:14

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Probability, the Normal Curve and z-Scores
8 Lectures
38:33

In this video we introduce the concept of probability as well as how to calculate the probability for different examples using the 'classical approach'.

Probability

04:15

In this video, the normal distribution and z scores are covered. First, properties of the normal distribution are described, including how the mean, median, mode are equal to zero and how the normal distribution is symmetrical. Next the areas under the curve are illustrated, closing with a demonstration of the 68, 95, 99.7 rule for values that are 1, 2, and 3 standard deviations away from the mean.

Normal Curve and z-Scores (68, 95, 99.7 Rule)

06:57

In this video lecture, we take a look at the properties of the z score normal distribution, including (1) that it is symmetrical, (2) that the mean, median, and mode are all equal to zero, and (3) that the standard deviation is equal to 1.

Preview
03:27

Properties of the z Score Normal Distribution

5 questions

This video reviews the answers to the quiz, Properties of the z-Score Normal Distribution.

Video Review of Quiz - Properties of the z-Score Normal Distribution

02:52

In this video lecture, z scores are covered, including how to solve for z scores for a number of different examples. Also illustrated is how the z score indicates the number of standard deviations a value is from the mean. For example, a z score of 1.5 indicates that a value is 1.5 standard deviations above the mean.

Solving for z-Scores

05:10

Solving for z-Scores

5 questions

Video Review of Quiz - Solving for z-Scores

04:22

In this video, we take a look at how to solve for an X given a z score, mean, and standard deviation.

Solving for X Given a z-Score

05:45

Solving for X Given a z-Score

5 questions

In this video, the answers are reviewed to the quiz, Solving for X Scores Given a z-Score.

Video Review of Quiz - Solving for X Scores Given a z-Score

05:45

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Hypothesis Testing
8 Lectures
40:19

This lecture begins our coverage on inferential statistics. In this video the null and alternative hypotheses are explained, with a focus on two-tailed tests.

Hypothesis Testing - Two Tailed Tests

04:59

In this video we take a look at several different examples of two-tailed hypothesis tests.

Two Tailed Hypothesis Tests - Examples

04:43

In this video the null and alternative hypotheses are covered for one-tailed tests. One tailed tests are used when the researcher / analyst is looking for a specific outcome (or direction of effect) and usually isn't interested if the opposite direction of effect is found.

Hypothesis Testing - One Tailed Tests

05:45

In this video we take a look at several different examples of one-tailed hypothesis tests.

One Tailed Hypothesis Tests - Examples

05:17

Hypothesis Tests

3 questions

This video covers Type I and Type II Errors with Examples

**Type I Error - Reject the null hypothesis when it is true.**

**Type II Error - Fail to reject (accept) the null hypothesis when it is false.**

Type I and Type II Errors Explained

07:51

In this video we take a detailed look at what a *p* value is. Examples using both alpha of .05 (most commonly used level of alpha) and .01 are included.

P-values are produced in statistics when analyses are run by computer (or calculator).

What is a P-Value?

06:01

In this video, the often-confused *p* value of .000 is covered. Why a *p* of .000 is often reported in computer output and exactly what it means is explained in this video.

P Value = .000 ???

02:40

This quiz covers p-values, including how to assess a hypothesis test based on different levels of alpha and what a p-value of .000 means.

P-values

3 questions

In this video, the concept of statistical power is illustrated.

**Power = The probability of rejecting the null hypothesis when it is false.**

Power

03:03

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Conclusion
1 Lecture
00:57

In this video we wrap up the course and introduce some of the other courses by Quantitative Specialists.

Conclusion

00:57

About the Instructor