Measures of dispersion, objectives, meaning of dispersion. As with other types of measures, there is more than one approach to defining such a measure. In the above cited example, we observe that i the scores of all the students in section a are ranging from 6. Dispersion is the state of getting dispersed or spread. Click here to view, download or print flexiprep exclusive measures of dispersion, objectives, meaning of dispersion, definition of various measures of dispersion, range, mean deviation from mean, variance, standard deviation.
Statistics measures of central tendency and dispersion class 2 session 2 oscarbarrera oscardavid. 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. The dispersion of a data set is the amount of variability seen in that data set. Cbse economics chapter 6 measures of dispersion class 11 notes economics in pdf are available for free download in mycbseguide mobile app. Connor defines measures of dispersion as dispersion is the measure extended to which individual items vary. The observations may be close to the center or they may be spread away from the center. A second characteristic of a distribution is the width of its spread around the central class. Two data sets can have the same mean but they can be entirely different.
Dispersion measures how the various elements behave with regards to some sort of central tendency, usually the mean. The measures of central tendency are not adequate to describe data. Absolute measures of dispersion are expressed in same units in which original data is presented but these measures cannot be used to compare the variations between the two series. The word dispersion has a technical meaning in statistics. Relative measures are not expressed in units but it is a pure number. Absolute measure of dispersion measure of dispersion. How can we then compare the dispersion of one group with. Two distributions with the same mean might differ very much in how closely the measurements are concentrated around the mean. 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. The range of a set of data is the largest measurement minus the smallest measurement. Weve already looked at the first two in the averages section, so lets move on to the other measures.
Measure of dispersion sample problems and solutions pdf. In statistics, there are many techniques that are applied to measure dispersion. Dispersion refers to the variation of the items around an average. This post investigates what these mean and how they work. In other words, if the measurements are in metres or seconds, so is the measure of dispersion. Practics question for ch 10 measures of dispersion exercise 1p 268. Measures of central tendency and dispersion paris school of. Another feature of the observation is how the observations are spread about the center. It includes range, standard deviation, quartile deviation, etc. The second type is the relative measure of dispersion, which measures the ratio unit. The range of a set of data is the largest measurement minus the. In other words, dispersion helps to understand the distribution of the data. We need quantitatively describe the dispersion in the data.
Dispersion is the scattered ness of the data series around it average. Central tendencyvariability measures of central tendency. Dispersion is the extent to which values in a distribution differ from the average of the distribution. Slide 3 central tendency measures do not reveal the variability present in the data. A measure of position is a method by which the position that a particular data value has within a given data set can be identified. Measures of central tendency are used because they represent centralized or middle values of the data. Measures of dispersion definition measures of dispersion. A measure of the spread of a distribution out from its central value. Measures of dispersion 8 a small value for a measure of dispersion indicates that the data are clustered closely the mean is therefore representative of the data. Measures of dispersion, a statistical technique, can be used to measure the disparity in the applicants of jamb in each states and geopolitical zones in nigeria.
It is amenable to mathematical manipulation because the algebraic signs are not ignored in its calculation as we ignore in case. Absolute dispersion method expresses the variations in terms of the average of. Introductory statistics lectures measures of variation. Statistical dispersion means the extent to which a numerical data is likely to vary about an average value. In analyzing, statistical data, it is often useful to have numbers describe the complete set of data. We give below some definitions of dispersion as given by different statisticians from time to time. Measures of statistical dispersion wyzant resources. Types of measures of dispersion,range, quartile deviation. Calculate the mean and the range of each of the following sets of data. Definition the sample zscore for a measurement x in a.
These types of dispersions can be used only in the comparing the variability of the series or distribution having the same units. Absolute dispersion method expresses the variations in terms of the average of deviations of observations like standard or means deviations. Dispersion, in general sense, also indicates the lack of uniformity in the size of items of a series. Measures of variation refer to a group of statistics that is intended to provide us with information on how a set of scores are distributed. The average measures the center of the data, and it is one aspect of observation. Measures of dispersion in research methodology tutorial 24. The first is the absolute measure, which measures the dispersion in the same statistical unit. Measures of dispersion although the range is easy to compute it is a crude measure of variability. Method validation and comparisons with some most important tools of dispersion measures e. Calculate the different measures of variability of a given ungrouped data.
Dispersion is a statistical term describing the size of the range of values expected for a particular variable. The other measures of central tendency median and mode and the guidelines for selecting the appropriate measure of central tendency will be dealt with in the subsequent issue. Statistics measures of central tendency and dispersion. In this lesson, you will read about the following measures of dispersion. These quantities measures the dispersion in the same units as the units of original data. Range, interquartile range, and standard deviation. Lets have a detailed look at absolute measures of dispersion and how they are used in six sigma practices. The best app for cbse students now provides measures of dispersion class 11 notes economics latest chapter wise notes for quick preparation of cbse exams and school based annual examinations. Measures of dispersion range, variance standard deviation co efficient of variation computation of the above statistics for raw and grouped data. Absolute measure of dispersion gives an idea about the amount of dispersion spread in a set of observations.
Definition central tendency measures do not reveal the variability present in the data. Following are some definitions defined by different experts on measures of dispersion. Notes of ecco measures of dispersion for class 11 chapter 6 download pdf. In problems involving descriptions and comparisons alone, the mean deviation can validly be applied. To quantify the extent of the variation, there are certain measures namely. Lesson initiator what is the purpose of finding an average. Copies of these textbooks may be downloaded and used as textbooks or for reference. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. In this paper we present an ontosemiotic macroscopic analysis of the measures of dispersion. Notes of ecco measures of dispersion for class 11 download pdf. In statistics, we answer these questions using measures of central tendency and measures of dispersion. Measures of dispersion explained magoosh statistics blog. Examples interquartile range, standard deviation, variance.
Thus to describe data, one needs to know the extent of variability. Absolute measures of dispersion is a great way of showing how quantitative data is spread relative to the center point of the data. How can we measure how much the data varies from the center. I mean, does your sample seem to represent the population well. Measures of dispersion are closely related to measures of central tendency. An absolute measure of dispersion contains the same unit as the original data set. Characteristics of a good measure of dispersion an ideal measure of dispersion is expected to possess the following properties 1. Looking specifically at range, variance, and standard deviation, this lesson explores the relationship between these measures and samples, populations, and what it says about your data. Those measures of dispersion whose units are same as the units of the given series is known as the absolute measure of dispersion. Dispersion is said to be significant when variation or lack of uniformity in the size of items of a series is great aid substantial.
Dispersion is the scatteredness of the data series around it average. Most measures of dispersion have the same units as the quantity being measured. Measures of variation enable comparison to be made of two or more series with regard to their variability. An examination of measures of variation is a logical extension of any description of a data set using the measures of central tendency that we examined in the previous chapter. Consider the following two sets of data which have the same mean, 25, and the same range. Example calculate the range for the data for quarterback a and quarterback b in the example above. Measuring market opportunity december 20 index investment strategy 2 the result is sometimes called crosssectional portfolio volatility. A large measure of dispersion indicates that the mean is not reliable it is not representative of the data. Should take individual values from the distribution into account so no value is left out.
630 1405 1301 806 992 558 239 845 1292 12 998 857 944 628 891 1230 582 1440 670 503 199 1397 540 890 1065 1028 1323 1065 25 880