Introduction to Statistics

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.

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."

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.

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

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

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

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

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.

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

In this video, we take a look at how to create a frequency distribution table. Frequency distribution tables are helpful for organizing a set of values. They allow for quick identification of several statistical values, such as the minimum and maximum values, and the mode for a set of data.

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.

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).

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

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.

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.

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

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.

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

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

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.

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

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.

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

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.

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).

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.

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

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

Here we take a look at how to calculate a correlation step-by-step. The next video illustrates how to test the correlation for statistical significance.

In this video, we take a look at how to test a correlation for significance, including how to write the results in a widely-accepted scientific format.

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