Central tendency and variability are two important properties of a distribution. Learn how to use Excel to quickly calculate these properties.
- [Instructor] Let's look at Probability Distributions. It assigns a probability to every possible outcome Think of each outcome as a possible value of a random variable. A probability distribution can be discrete, and so it's random variable is a set of possible outcomes that you can count. It's very easy to assign a probability to each one, like a coin toss or rolling a die. And here's a simple example. Tossing a coin. to it as X. The possible values are head and tail. and tail equals zero. are one and zero. And here's a picture of the probability distribution for tossing a fair coin. probability of occurrence, and that probability is 1/2. This type of probability distribution is called a probability mass function. A probability distribution can be continuous. That means, it's random variable is on a continuum. The possible outcomes are not countable. The random variable can take on any value between two specified values. Here's an example of what I mean. When we measure a person's height, the rulers precision limits the accuracy. So probability is assigned to an interval, not to an exact number. For example, instead of the probability that a person is 69 inches tall, we'd be concerned with the probability that their height is between 68 inches and 70 inches. These kinds of distributions look like this, possible values on a continuum, the number of outcomes is uncountable. This type of probability distribution is called a probability density function. Note that probability density is on the y-axis. Probability density is a math concept that enables us to use area under the curve, as probability. A probability density function is often based on a complex equation. Every distribution has a mean and a variance. And a probability distribution is no exception. Calculating the mean and variance is easier for a discrete For continuous distribution we'd have to get into some sophisticated mathematics, and we won't do that. is also called the expected value. To calculate the expected value, you multiply each outcome times it's probability, add the products, and the result is the expected value. Applying all this to tossing a coin equal to .5, so the expected value is zero times .5, plus one times .05, which comes out to .5. To calculate the variance you subtract the expected value from each outcome and square the differences. by it's corresponding probability, and the sum of the results is the variance, also labeled as V(x)). It's square root is the standard deviation, sigma. And applying this to tossing a coin, the variance, zero minus .5 squared times .5, plus one minus .5 squared times .5, And the standard deviation is the square root of .25, which is .5. And now the mean and the variance for rolling a die. The expected value as you can see, works out to 3.5. And the variance is 2.92. The standard deviation is the square root of 2.92, or 1.71. In summation, we talked about probability distributions and how they can be discrete or continuous, and we showed how to calculate the mean and the variance of the discrete distribution.
- Explain how to calculate simple probability.
- Review the Excel statistical formulas for finding mean, median, and mode.
- Differentiate statistical nomenclature when calculating variance.
- Identify components when graphing frequency polygons.
- Explain how t-distributions operate.
- Describe the process of determining a chi-square.