Aug 09, 20 measure of dispersion part i range, quartile deviation, interquartile deviation, mean deviation 1. Consider the following two sets of data which have the same mean, 25, and the same range, 10, but obvious di erences in the pattern of variability. Class 11 statistics economics chapter 6 measures of dispersion. Measures of dispersion and skewness a measure of dispersion indicates how varied the observations are in a collection. Understanding measures of dispersion in statistics. Of all the measures of dispersion, the range is the easiest to determine. Averages are also called measures of central tendency. Measures of dispersion mathematics alevel revision. Measures of dispersion definition of range page 232 definition 8. It is commonly used as a preliminary indicator of dispersion.
Three friends, ram, rahim and maria are chatting over a cup of tea. While drawing conclusions and inferences to forecast and compare two or more than two data or series. Central tendency gets at the typical score on the variable, while dispersion gets at how much variety there is in the scores. A small value indicates that the observations are not too different from each other, while a large value indicates that the observations are very different from each other. When describing the scores on a single variable, it is customary to report on both the central. In statistics, dispersion is the extent to which a distribution is stretched or squeezed. Measures of dispersion are closely related to measures of central tendency. In order to measure this scatter, statistical devices called measures of dispersion are calculated.
Measures of dispersion article about measures of dispersion. Calculate the absolute and relative values of dispersion. The analysis of relaxation dispersion relax nmr analysis. Jun 30, 2015 chapter 11,measures of dispersionstatistics 1. Range is the simplest possible measure of dispersion and is defined as the difference between the values of the extreme items of a series. Range range is defined as the difference between the maximum and the minimum observation of the given data. Divide this total by n1 to get the sample variance. The assumption involves standard deviation, variance, and interval strength. Measures of dispersion include range, interquartile range, variance, standard deviation and absolute deviation. Such a number is called a measure of central tendency. The coefficients of dispersion are calculated along with the measure of dispersion when two series are compared which differ widely in their averages.
We learned that dispersion, or variability, is how spread out our data is. Measures of dispersion notes chapter 12 section 3 page 1. Measures of central tendency and dispersion paris school of. In all the cases the sum of the observations will be the same. In this chapter, we will discuss measures of dispersion in an order that will ultimately bring us to the two measures used to the virtual exclusion of the others, the variance and its positive square root, the standard deviation. Meanwhile, a value of zero indicates the absence of variation in the. Measures of dispersion although the range is easy to compute it is a crude measure of variability. Additionally, it covers distribution of data, which includes standard deviation and interquartile range. Shakehand with life promoting quality culture in every sphere of human life page 2. The measure of dispersion shows the homogeneity or the heterogeneity of the distribution of the observations. Measure of dispersion part i range, quartile deviation, interquartile deviation, mean deviation 1. Chapter learning objectives explain the purpose of measures of dispersion compute and interpret these measures range r, interquartile range qor iqr standard deviation s, variance s2 select an appropriate measure of dispersion and correctly calculate and interpret the statistic describe and explain the mathematical. Statistics measures of central tendency and dispersion class 2. Measures of central tendency and dispersion pdf free download.
In this chapter you will study those measures, which seek to quantify variability of the data. Calculate the difference between each value and the mean. For the study of dispersion, we need some measures which show whether the dispersion is small or large. Range is the interval between the highest and the lowest score. Measures of dispersion tell you how widely spread out the values are most common are range, standard deviation, and variance range the range of a data set is the difference between the maximum and minimum values in the set example. Dispersion, pg 128 the extent of clustering or spread of the scores around the mean. Measures of dispersion are called averages of the second order because in precise study of dispersion, the deviations of the size of items from a measure of central tendency are calculated ignoring the signs and then these deviations are averaged. Ncert solutions for class 11 statistics economics chapter 6 measures of dispersion pdf free download. This document is highly rated by class 11 students and has been viewed 193 times. Those are the kinds of statistics this chapter discusses. The chapter also covers measures of central tendencymean, median, as well as mode. Measures of location and dispersion and their appropriate uses. The first is the absolute measure, which measures the dispersion in the same statistical unit. Dispersion is a measure of the variation of the items from central value.
It is also the most important because of being the only measure of dispersion amenable to algebraic treatment. Measures of dispersion, pg 128 measures of variability that addresses degree of clustering of the scores around the mean. Range, pg 129 simplest measure of dispersion that compares the highest score and the lowest score achieved for a given set of scores. You can skip questions if you would like and come back to.
Ncert solution for class 11 commerce statistics chapter 6 measures of dispersion furnishes us with an allinclusive data to all the concepts. Practics question for ch 10 measures of dispersion exercise 1p 268. While measures of central tendency are used to estimate normal values of a dataset, measures of dispersion are important for describing the spread of the data, or its variation around a central value. There are four commonly used measures to indicate the variability or dispersion within a set of measures. The best educational study material, books, notes, solutions solved questions answers and sample papers in pdf files free to download for schools, teachers, tutors and students for better exam result. In statistics, there are many techniques that are applied to measure dispersion. A modern student of statistics is mainly interested in the study of variability and uncertainty. Two distinct samples may have the same mean or median, but completely different levels of variability, or vice versa. Range maximum minimum sometimes the range is presented by stating the smallest and the largest values. Measures of statistical dispersion wyzant resources. Ncert solution for class 11 statistics chapter 6 measures. Measures of dispersion in research methodology tutorial. The measures of dispersion is important to compare uniformity, consistency and reliability amongst variables series.
Take the square root of the sample variance to get the sample standard deviation. Practics question for ch 10 measures of dispersion exercise 1. Statistics is a part of mathematics that deals with the gathering, formation, analysis, elucidation and presentation of data. In 4, 6, 9, 3, 7 the lowest value is 3, and the highest is 9. Cbse class 11 economics revision notes chapter 6 measures of dispersion class 11 notes economics. In a town, 25% of the persons earned more than rs 45,000 whereas 75% earned more than 18,000.
View notes measures of dispersion notes from math 120 at university of nevada, las vegas. Measures of dispersion definition measures of dispersion. Statistical dispersion means the extent to which a numerical data is likely to vary about an average value. A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Out of several measures of dispersion, the most frequently used measure is standard deviation. Chapter 4 measures of dispersion range quartiles variance standard deviation coefficient of variation. Jun 11, 2009 in statistics, dispersion has two measure types. Scribd is the worlds largest social reading and publishing site. Dispersion is the state of getting dispersed or spread. Types of measures of dispersion,range, quartile deviation. However, that value does not reveal the variability present in the data. Measures of dispersion class 11 notes edurev is made by best teachers of class 11. Those measures of dispersion whose units are same as the units of the given series is known as the absolute measure of dispersion.
Measures of ccentral tendency and dispersion pdf free download important term and concepts. Notes of ecco measures of dispersion for class 11 download pdf. In the previous chapter, you have studied how to sum up the data into a single representative value. Measure of dispersion part1 class 11 economics notes website. Suppose you have four datasets of the same size and the mean is also same, say, m. Here, the measure of central tendency is not giving a clear. Calculate the mean and the range of each of the following sets of data. Look at this table that shows the number of students who got a mark out of 30 for a class test. Dispersion measures how the various elements behave with regards to some sort of central tendency, usually the mean. This document is highly rated by class 11 students and has been viewed 3870 times. The standard deviation steps for calculating standard deviation 1. In this video lesson, we talked about dispersion and skewness.
The measures of central tendency are not adequate to describe data. Some measures of dispersion depend upon the spread of values whereas some calculate the variation of values from a central value. Lets compare it to the variance of this lessdispersed data set. Notes on measures of dispersion grade 11 economics. In this article, we will consider measures of dispersion, which describe how the data is dispersed around a central value. Dispersion refers to the variation of the items around an average. Objectives of dispersion a to determine the reliability of an average. Range is a measure of variability or scatteredness of. Sep 14, 2014 dispersion, pg 128 the extent of clustering or spread of the scores around the mean. The measures of dispersion you have just seen differ in ways that will help determine which one is most useful in a particular situation. Measures of dispersion alevel mathematics statistics revision section of revision maths covering standard deviation, variance and quartiles. Calculate the range, variance and standard deviation of a set of ungrouped values.
Introduction in addition to finding measures of central tendency for a set of scores, we also calculate measures of dispersion to aid us in describing the data. Describe and interpret numerically and verbally the dispersion or spread of values in a data set. Absolute and relative measures of dispersion when dispersion of the series is expressed in terms of the original unit of the series, it is called absolute measure of dispersion. Absolute and relative measures of dispersion when dispersion of the series is expressed in terms of the original unit of the series, it is called absolute measure o. So the two mean deviations computed above indicate almost similar dispersion.
For the measures of dispersion considered, we will rely on the mean as the standard measure of central tendency, and we will. Index, a measure of dispersion of individuals springerlink. We use central values and say that the observation having higher greater central values are better than the others having. Measure of dispersion part i range, quartile deviation. Two data sets can have the same mean but they can be entirely different.
Measure of dispersion part1 class 11 economics youtube. Thus to describe data, one needs to know the extent of variability. The dispersion coefficient is also used when two series with different measurement unit are compared. These types of dispersions can be used only in the comparing the variability of the. The second type is the relative measure of dispersion, which measures the ratio unit. It is a value which is typical or representative of a set of data. The dispersion of heavy particles line in an isotropic and incompressible threedimensional turbulent flow has been studied using the kinematic simulation techniques to find out the evolution of the line fractal dimension.
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