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A measure of variability is a statistic that talks more about the amount of dispersion within a set of data. It describes how much the values of the data set are spread. Where else, a measure of central tendency describes a typical value of a data set. Measures of variability describe how far the data points fall from the center. Hence, when we talk about variability, we generally considered as the context in which values are distributed. When there is low dispersion indicates that the points of a data tend to cluster around the center tightly. A high dispersion means that the data points tend to fall further away from the center.
Variability, spread, and dispersion are similar words that talk more about the width of a given distribution. The well-known measures of variability are the standard deviation, variance, range, and the interquartile range. In this post, we shall discuss the four common measures of variability as mentioned earlier. This post will be of great importance in determining which of the above measures of variability is suitable for your data.
Standard Deviation
The standard deviation is the typical or standard difference between the mean and each data point. A smaller standard deviation means that the values of a data set are closely grouped. On the other hand, a larger standard deviation indicates that the values are spread out more hence the standard distance is greater. Conveniently, the interpretation of standard deviation is easier because it uses the original units of the given data. It's much accurate to say that standard deviation is the most commonly used measure of variability. A standard deviation is typically the square root of the variance. The standard deviation is denoted as σ while the sample estimate is denoted as s.
Variance
A variance is an average square of the difference between values from their mean. This measure of variability includes each of all values given in comparison to the mean. In calculating variance, two formulas can be used depending on whether you are calculating a variance of a sample of an estimate or the entire population.
Range
A range is the easiest and the most straightforward measure of variability to understand and calculate. When we talk about a range of a dataset, we mean the difference between the dataset's largest value and the smallest value. If the data set has a wide range, it means that such a dataset has high variability and vice versa. A range is based on two most extreme values which make it highly susceptible to outliers. A range is also affected by the size of the dataset. The larger the sample size, the more chances of obtaining the extreme values.
Interquartile Range
The interquartile range is the middle half of median of a given data. Data can be divided into quarters known as quartiles. A denoted from low to high quartile, Q1, Q2,Q3, and Q4.Q1 is the quarter with the smallest values while Q4 is the quarter with the highest values.
Just as the median is a string measure of central tendency, interquartile range is a reliable measure of variability. Interquartile and medians are not susceptible to outliers since they do not depend on every value. In case you are looking for a reliable measure of variability on skewed distributions, then interquartile is the best option for you.
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