Note that deviation is always calculated by taking the mean of the reference and it always involves positive values. The standard deviation is known to be one of the most preferred methods to measure deviation as compared to the other measures of dispersion. Mean deviation comes as an improvement over the range and it basically measures the deviations from a value generally known as mean or median. Although the mean deviation about mode can be easily calculated, the mean deviation about mean and median are most commonly used. The mean deviation can be mean, median or mode. ![]() Usually mean deviation is used to understand the dispersion of data from the given measures of central tendency. Mean Deviation is the mean of all the absolute values of the differences between the numbers of a set also known as statistical data and their mean or median. ![]() Quartile deviation or semi-inter-quartile deviation is The middle number between the median and the largest number is called the third quartile, (Q3). The median of the data set is called the second quartile, (Q2). The middle number between the smallest number and the median of the data is called the first quartile, (Q1). In a set of data, there is always the smallest number, largest number, and median. Quartile divides a set of data into four equal parts. The word quartile is derived from the word quarter which means one-fourth. The range of Batsman A is more than Batsman B, so the data in the case of Batsman A is more dispersed than Batsman B. Thus, the range of Batsman A = 117-0 = 117 whereas the range of Batsman B = 60-40 = 20. Let us suppose two batsmen have their minimum and maximum runs scored in a series. The range gives a rough idea of how scattered data is, but we need other measures of variability to find the dispersion of data from measures of central tendency. The difference in the minimum and maximum values of each series is called range. Below are the types of measures of dispersion: The dispersion always depends on the observations and types of measures of central tendency. The fluctuations in the observations do not affect measures of dispersion. Understanding and calculation of measures of dispersion are easy. It is defined rigidly and depends on all the observations. It also describes the variation of data from one another. Measures of dispersion specify the homogeneity or heterogeneity of the scattered data. ![]() The measure of dispersion is always a non-negative real number that is zero if all the data are the same and increases as the data becomes more diverse. It is also called variability, scatter, spread.Īs we know, dispersion is a way of describing how scattered a set of data is. Variance, standard deviation, and interquartile are types of dispersion. Example of widely scattered data - 0, 30, 60, 90, 120, … and tightly clustered data of small value - 1, 2, 2, 3, 3, 4, 4. ![]() A set of data having a large value is always widely scattered or tightly clustered. In short, it is the distribution of data. In statistics, the extent to which the numerical data are distributed or squeezed about an average value is called dispersion. The word dispersion stands for ‘distribution’ of things over a wide area.
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