Descriptive Statistics > Bimodal Distribution: Two Peaks. Data distributions in statistics can have one peak, or they can have several peaks. The type of distribution you might be familiar with seeing is the normal distribution, or bell curve, which has one peak. The bimodal distribution has two peaks. Watch the video for an overview of the bimodal distribution: Watch this video on YouTube. Can’t see the video? Click here. Bimodal distribution showing two normal distribution curves combined, to show peaks. Image credit: Maksim|Wikimedia Commons The “bi” in bimodal distribution refers to ..read more

Probability and Statistics> TI 83 for Statistics TI 83 for Statistics: Overview. The TI 83 graphing calculator is a popular hand held calculator that’s most often recommended for stats students. The calculator has an array of functions that can help you with your elementary stats or AP stats course. For example, the calculator has a built in function for linear regression. Try to figure that out by hand will take you upwards of thirty minutes (even for a small data set). But you can solve it on the TI 83 in a few seconds, once you have entered your data into a list. Don’t have a TI83 calcul ..read more

Probability Distribution: List of Statistical Distributions > Ferreri distributions (distribuzione di Ferreri) are a system of probability distributions described by Ferreri. The distributions have probability density functions (PDFs) is a four-parameter distribution of the form [1]: where (a, b, c, ξ) are the four parameters: ξ is the mean. If c = 1, β2 < 3; If  c = – 1, β2 > 3. As a increases, the distribution approaches a normal distribution [2]. The rth absolute moment about ξ is While the distribution is usually attributed to Ferreri (1964), there is a mention of the ..read more

Statistics Definitions > A frequency in statistics is the number of times an event or observation happened in an experiment or study. It can also be defined simply as a count of a certain event. For example, you might conduct a survey of pet owners to see how many people owned certain kinds of pets. If 16 people responded that they owned a dog, then 16 is the frequency (the count of the number of people who own dogs). It’s often easier to understand your results if you create a graph or table such as a frequency chart. This relative frequency table shows survey results — counts — for pet o ..read more

Statistics Definitions > What is Central Tendency? Central tendency (sometimes called measure of location, central location, or just center), attempts to describe an entire set of data with one figure — a statistic such as an average amount or a median price. Central tendency doesn’t tell you specifics about the individual pieces of data, but it does give you an overall picture of what is going on anthe entire data set. There are three major ways to show central tendency: mean, mode and median. Central Tendency Measures 1. The Mean The mean is the average of a set of numbers. To find it, ad ..read more

Probability Distributions > There isn’t a universal definition for the “reciprocal distribution.” Definitions from the literature include: Any distribution of a reciprocal of a random variable [1]). A reciprocal continuous random variable [2]. A synonym for the logarithmic distribution [3]. That said, most PDFs for a reciprocal distribution involve a logarithm in one form or another: for pink noise, distributions of mantissas (the part of a logarithm that follows the decimal point), or the under-workings of Benford’s law. Of all the different versions of the probability distribution funct ..read more

Statistics Definitions > Sample percentages are obtained from surveying a fraction of the population. When you estimate a percentage from a fraction of a population, that’s called a sample percentage. Let’s say you wanted to find out how many people in the United States are women. According to the Census bureau, that figure — the population percentage — is 50.5%. But it’s not often that kind of data is available, so you may need to conduct a survey to estimate this information. Sample Percentage Example If you wanted to find out the percentage of females that feel comfortable going to the ..read more

Hypothesis Testing > What is a Rejection Region? The rejection regions in a two-tailed t-distribution. Image: ETSU.edu A rejection region (also called a critical region) is an area of a graph where you would reject the null hypothesis if your test results fall into that area. In other words, if your results fall into that area then they are statistically significant. Watch the video for an overview: Watch this video on YouTube. The main purpose of statistics is to test theories or results from experiments. For example, you might have invented a new fertilizer that you think makes plan ..read more

Statistics Definitions > Pearson’s Coefficient of Skewness Contents: Definition and Examples Interpretation Excel Steps Watch the video for an example: Watch this video on YouTube. see the video? Click here. What is Pearson’s Coefficient of Skewness? Karl Pearson developed two methods to find skewness in a sample. Pearson’s Coefficient of Skewness #1 uses the mode. The formula is: Where = the mean, Mo = the mode and s = the standard deviation for the sample. See: Pearson Mode Skewness. Pearson’s Coefficient of Skewness #2 uses the median. The formula is: Where = the mean, Mo = the m ..read more

Statistics Definitions > Decile Deciles break up a set of data into tenths. They are similar to quartiles. But while quartiles sort data into four quarters, data is sorted into ten equal parts: The 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th and 100th percentiles. Watch the video for an overview: Watch this video on YouTube. A decile rank assigns a number to each tenth: Decile Rank Percentile 1 10th 2 20th 3 30th 4 40th 5 50th 6 60th 7 70th 8 80th 9 90th The higher your place in the above rankings, the higher your overall ranking. For example, if you were in ..read more