The standard deviation is the commonly used measure of variability when working with numeric data. It indicates how much, on average, each score in a set varies from the mean value of that set. It is usually represented by “s” or SD and is indicated as a +/- value. This single value demonstrates how much variability or dispersion is among scores in a set. To calculate the value, we must compute the deviation of each score from the mean and…
The range, which is the simplest and least precise of the measures of variability, is determined by subtracting the lowest score in a set of data from the highest score. It provides a measure that considers the two most extreme scores in a set without accounting for any of the other scores between the extremes. The formula for the range is r = h – l, Where r = range, h = the highest score in the set, and l…
Measures of variability, such as the range, variance, and standard deviation, are types of descriptive statistics that complement the measures of central tendency in describing data sets. These measures of variability reflect how scores differ or are spread or dispersed from one another. A more precise definition is the distance or amount a score in a data set differs from the typical score in the set, usually the mean. The three most common forms of variability are the range, variance,…
A common struggle for novice statisticians is choosing a measure of central tendency that is most appropriate in a given situation. It depends on the type of data you have and some basic data distribution characteristics. If your data values are categories or descriptive words (e.g., political party, eye color, the country where you were born), the mode is your best option. Categorical data is information that fits into finite options in which only one option can be true at…
The mode is the central tendency measure that indicates the data point that occurs most frequently in a set of scores. It measures the frequency of occurrence of each unique value and denotes the score that has the highest frequency. The data points that the mode can describe can be numeric (e.g., height in cm or weight in pounds) or word-based (e.g., eye color, the city in which you live). The data points are organized somehow, and the frequency of…
The median is another measure of central tendency representing the “middle score” in a set. It’s the point in a score distribution in which 50% of the scores fall below it and 50% fall above it. The median is usually represented by Md. but can sometimes be represented by M. Computing the median is a two-step process: List all the scores in order, starting with the highest value and progressing to the lowest. For example: 100, 88, 76, 65, 40, 25,…
The mean is the most commonly used measure of central tendency and is considered a descriptive statistic. In practical terms, it is the sum of all the values in a data set divided by the number of values. It is a single value that can summarize the value of many of the scores in the data set. It represents the middle of the score distribution, hence the term “measure of central tendency.” A simple version of the formula would be:…
Inferential statistics allow us to make decisions about a large group (usually referred to as a population) based upon observations made within a small group selected from that population (usually referred to as a sample. This ability to infer something about a population based upon a sample allows a deeper understanding of data beyond what descriptive statistics alone can offer. Sometimes knowing the mean of a group of scores is enough information. Still, inferential statistics allows us to compare the…