Measures of Variability

-

Measures of Variability

       Measures of central tendency, such as the mean and the median described in article 2 (22.02.2019) provide useful information. But it is important to recognize that these measures are limited and, by themselves, do not provide a great deal of information.

There are three measures of dispersion that researchers typically examine: the range, the variance, and the standard deviation. Of these, the standard deviation is perhaps the most informative and certainly the most widely used.

Range

The range is simply the difference between the largest score (the maximum value) and the smallest score (the minimum value) of a distribution.

Squared deviation

The difference between an individual score in a distribution and the mean for the distribution, squared.

Variance

The variance provides a statistical average of the amount of dispersion in a distribution of scores. The other word sum of the squared deviations divided by the number of cases in the population, or by the number of cases minus one in the sample.

Standard Deviation
The best way to understand a standard deviation is to consider what the two words mean. Deviation, in this case, refers to the difference between an individual score in a distribution and the average score for the distribution. So if the average score for a distribution is 10, and an individual child has a score of 12, the deviation is 2. The other word in the term standard deviation is standard.

Variance and Standard Deviation Formulas


Box plot
A graphic representation of the distribution of scores on a variable that includes the range, the median, and the interquartile range.

Interquartile range (IQR)

The difference between the 75th percentile and 25th percentile scores in a distribution.

μ          The population mean.
X         An individual score in a distribution.
s2         The sample variance.
s           The sample standard deviation.
σ          The population standard deviation.
σ2           The population variance.
SS        The sum of squares, or sum of squared deviations.
n          The number of cases in the sample.
N         The number of cases in the population.

Comments

Post a Comment

Popular posts from this blog

Basics of Statistics

-
In this Article, review some of the fundamental research principles and terminology including the distinction between samples and populations, methods of sampling, types of variables, and the distinction between inferential and descriptive statistics. Statistic: A characteristic, or value, derived from sample data. Descriptive statistics: Statistics used to describe the characteristics of a distribution of scores. Inferential statistics: Statistics, derived from sample data that are used to make inferences about the population from which the sample was drawn. Parameter: A value, or values, derived from population data. A population is an individual or group that represents all the members of a certain group or Category of interest. A sample is a subset drawn from the larger population. Sample: A collection of cases selected from a larger population. Random sample (or random sampling): Selecting cases from a population in a manner that ensures each me...
Read more

Madaline

-
Image
Multiple Adaptive Linear Neuron Madaline which stands for Multiple Adaptive Linear Neuron, is a network which consists of many Adalines in parallel. It will have a single output unit. Some important points about Madaline are as follows ·         It is just like a multilayer perceptron, where Adaline will act as a hidden unit between the input and the Madaline layer. ·         The weights and the bias between the input and Adaline layers, as in we see in the Adaline architecture, are adjustable. ·         The Adaline and Madaline layers have fixed weights and bias of 1. ·        Training can be done with the help of Delta rule. Architecture The architecture of Madaline consists of “n” neurons of the input layer, “m” neurons of the Adaline layer, and 1 neuron of the Madaline layer. The Adaline layer can be considered as the hidden layer as...
Read more