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What are the characteristics, uses, advantages, and disadvantages of each of the measures of location and measures of dispersion? it varies widely from sample to sample. Types of Measures of Dispersion. It is defined as the difference between the largest and the smallest item in a given distribution. how far scores vary and differ from one another. 1) It should be easy to calculate and simple to follow. Like, Kilograms, Rupees, Centimeters, Marks etc. It is a crude measure because it is only based on two extreme values (highest and lowest). Absolute Measures of Dispersion: Quartile Deviation In terms of absolute measures of dispersion, quartile deviation is half of the difference between the first and third quartile, Q1 and Q3. It is important because it exhaustively includes all the possibilities. Measures of dispersion give a single value indicating the degree of consistency or uniformity of distribution. Graphical Measure of Dispersion × The way to calculate the measure of dispersion by figures and graphs. In simple terms, it shows how squeezed or scattered the variable is. Characteristics of Measures of Dispersion: (a) Range: 1. What are the basic properties that a suitable measure of income inequality should possess? Characteristics of a good measure of dispersion An ideal measure of dispersion is expected to possess the following properties The below mentioned article provides a close view on the measures of dispersion in statistics. It gives us an idea about the extent to which individual items vary from one another and from the central value. Merits and Demerits of Quartile Deviation. 4. There are different measures of dispersion like the range, the quartile deviation, the mean deviation and the standard deviation. 5. These measures are calculated for the comparison of dispersion in two or more than two sets of observations. Its value may be greatly changed if an extreme value (either lowest or highest) is withdrawn or a fresh value is added. PreserveArticles.com is an online article publishing site that helps you to submit your knowledge so that it may be preserved for eternity. Let’s start with a funny (and not so realistic) example. Measures of Dispersion. The measure of dispersion shows the homogeneity or the heterogeneity of the distribution of the observations. They speak of the reliability, or dependability of the average value of a series. The first quartile is derived as (Q), the middle digit (Q1) connects the least number with the median of the data. You’re kind of an adventurous person and you don’t have too many capricious demands regarding where you want to live next. For calculating mean deviation, deviations can be taken from any average. There are mainly two types of measures of dispersion. Characteristics of a good measure of dispersion The properties of a good ideal measure of dispersion are the same as those of measure of central tendency. What Are the Merits and Demerits of Range? The measures of dispersion which are expressed in terms of the original units of the observations are termed as absolute measures. So, dispersion measures the extent to which different items tend to disperse away from the central tendency. TOS According to Yule and Kendall, they are as follows. Surprisingly, the term statistic first came into use as late as 1817. It affords an estimate of the phenomena to which the given (original) data relate. Measures Of Dispersion: Dispersion is the extent to which values in a distribution differ from the average of the distribution. Objective of dispersion. It is defined as the difference between the Upper Quartile and Lower Quartile of a given distribution. Measures of Dispersion: The degree of spread determines the probability and the level of confidence that one can have on the results obtained from the measures of central tendency. It is the simplest method of measurement of dispersion. It is useful as a rough measure of variance. It provides a broad picture of the data at a glance. It should be capable of further mathematical treatment and statistical analysis. Our mission is to liberate knowledge. Characteristics of a good measure of dispersion An ideal measure of dispersion is expected to possess the following properties 1. This curve is often used to measure the inequalities of income or wealth in a society. 3. It is simple to calculate and easy to understand. These measures are free of the units in which the original data is measured. It may not be possible to use this method in case of Open ended series. The measure should be rigidly defined. A small value of dispersion means low variation between observations and average. The standard deviation is given as, σ = [(Σi (yi – ȳ) ⁄ n] ½ = [(Σ i yi 2 ⁄ n) – ȳ 2] ½. Especially in the financial analysis of business and Medical, these measures of dispersion can prove very useful. Ignoring + and – signs is bad from the mathematical viewpoint. Hence, the method of dispersion helps to find the correct variation of the data. It is not capable of further mathematical treatment. 2. It is very easy to calculate and simple to understand. In this video, I have continued to explain some more statistical concepts from MEASURE phase of the Six Sigma. Measures of dispersion go hand in hand with the measures of central tendency. 3. Following Are the Relative Measure of Dispersion: It refers to the ratio of the difference between two extreme items of the distribution to their sum. According to Yule and Kendall, they are as follows 1) It should be easy to calculate and simple to follow. The Lorenz Curve is a graphic method of measuring estimated dispersion. It should be based on all the items. All the articles you read in this site are contributed by users like you, with a single vision to liberate knowledge. But the merits and demerits common to all types of measures of dispersion are outlined as under: Merits. Reports of central tendency are commonly supplemented and complemented by including a measure of dispersion. The measure of dispersion indicates the scattering of data. It means the average is a good representative of observation and very reliable. We’ve started colonizing and populating new planets. It indicates the relationship between the standard deviation and the arithmetic mean expressed in terms of percentage. It is less affected by extreme values so, it a superior to ‘Range’. Hence, Dispersion is defined as the measure of scattering or variation of the items from the central value. It facilitates to determine the nature and cause of variation in order to control the variation itself. It explains the disparity of data from one another, delivering a precise view of the distribution of data. You’re bored of living on Earth and decide to take off towards another planet. The scatterness or variation of observations from their average are called the dispersion. It is difficult to compute when the mean or median is in fraction. Notes on the types of Absolute Measures of Dispersion, Notes on the Usefulness of Measures of Dispersion, Notes on Absolute and Relative measures of Dispersion, Notes on the merits and demerits of Standard Deviation. Mean deviation is the arithmetic mean (average) of deviations. Content Guidelines It is known as Semi-Inter-Quartile Range, i.e. It refers to the ratio of the difference between Upper Quartile and Lower Quartile of a distribution to their sum. It is affected considerably by fluctuations of sampling. It is not capable of further algebraic treatment or statistical analysis. Measures of Dispersion . Common measures of dispersion are as follows: Range: The two endpoints between which all the values of a data set fall is called a range. It should be based on all the items. The variation can be measured in different numerical measures, namely: (i) Range – It is the simplest method of measurement of dispersion and defines the difference between the largest and the smallest item in a given distribution. A higher value of dispersion means greater deviation among the observations. half of the difference between the upper quartile and lower quartile. 3) It should be based on all the items so as to be more representative. (iii) Mean Deviation-Mean deviation is the arithmetic mean (average) of deviations ⎜D⎜of observations from a central value {Mean or Median}. first reply Measures of location and measures of dispersion are two different ways of describing quantitative variables. It should be easy to calculate & simple to understand. Measures of location are often known as averages. There are two main types of dispersion methods in statistics which are: Absolute Measure of Dispersion It should be rigidly defined 2. Essential Characteristics of Dispersion “From the foregoing definitions, the essential characteristics of a measure of dispersion can be outlined as under: It consists of different methods through which variations can be measured in quantitative manner. 3. spread of scores, i.e. Requirements of a good measure of Dispersion: For measure of dispersion to be classified as a good measure of dispersion, It must have the following characteristics. It should not be unduly affected by sampling fluctuations. No special knowledge is needed while calculating range. Range – A simple calculation of the dispersion in a set of scores. Standard deviation is the Square Root of the Arithmetic Average of the squared of the deviations measured from the mean. It is not much affected by extreme values. Since measures of dispersion are usually called as averages of the second order, they should possess all the qualities of a good average. The range is simple to understand and easy to calculate because its value is determined by the two extreme items. Different types of measures of dispersion It is used to compare two data with respect to stability (or uniformity or consistency or homogeneity). The measure of dispersion displays and gives us an idea about the variation and central value of an individual item. Comparisons of Measures of Dispersion When data are described by a measure of central tendency (mean, median, or mode), all the scores are summarized by a single value. An ideal measure of dispersion is to satisfy the following characteristics. It cannot be calculated in the case of open-ended series. It explains the disparity of data from one another delivering a precise view of the distribution of data. It deals with a statistical series. 2. In statistics, the measures of dispersion help to interpret the variability of data i.e. They’re also essential to reading any data set because they show you how variable your data is. In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. It is based on all the observations of the series and not only on the limits like Range and QD. It can be used even in case of open-end distribution. Apart from a numerical value, graphics method are also applied for estimating dispersion. The measure of dispersion displays and gives us an idea about the variation and central value of an individual item. As the name suggests, the measures of dispersion show the extent of variability and the scattering of the data points. It should lend itself for algebraic manipulation. The median of a data set is the (Q2) second quartile. Range is significantly affected by fluctuations of sampling i.e. It should be rigidly defined 2. 2) It should be rigidly defined: For the same data, all the methods should produce the same result. The measure of dispersion indicates the scattering of data. i. It should be based on all observations in the data set.. ii. The main idea of the measures of dispersion is to get to know how the data are spread and how much the data points vary from the average value. PreserveArticles.com: Preserving Your Articles for Eternity, Brief notes on the definitions, importance and properties of Dispersion. 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