Measures of central tendency and dispersion pdf free download. Measures of dispersion, also known as variation, tell us how spread out or compact the data tends to be. The more similar the scores are to each other, the lower the measure of. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. Form the above example it is obvious that a measure of central tendency alone. Measures of centrality and dispersion this module introduces key concepts of summarizing data. In this lecture we will cover the three basic measures of dispersion. Measures of statistical dispersion wyzant resources. The range is simply the difference between the largest and smallest value in a data set. This topic is usually discussed in the context of academic. The average measures the center of the data, and it is one aspect of observation.
The measurement of the scatter of the given data about the average is said to be a measure of dispersion or scatter. Types of measures of dispersion measures of dispersion range r mean deviation md variance standard deviation sd 8. Central tendency gets at the typical score on the variable, while dispersion gets at how much variety there is in the scores. However, the present discussion will be limited to the three types of. A measure of statistical dispersion is a real number that is zero if all the data are identical, and increases as the data becomes more diverse. Arithmetic mean median mode you should note that ther e ar e two mor e types of averages i. If the mean is the appropriate measure of central tendency, then the standard deviation sd is likely to be a good measure of spread, but the median absolute difference mad migh.
There are various types of measures of dispersion like range, mean deviation, standard deviation. Averages are also called measures of central tendency. Jan 17, 2015 skewness a fundamental task in many statistical analyses is to characterize the location and variability of a data set measures of central tendency vs. The first brought things together while the second caused them to part. To facilitate the use of other statistical measures. Relative measures of dispersion are obtained as ratios or percentages of the average. Measures of dispersion are closely related to measures of central tendency. Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables.
Definition of measure of dispersion in statistics, dispersion also called variability, scatter, or spread is the extent to which a distribution is stretched or squeezed. Calculating variance involves squaring the differences deviations between the element and the mean and this makes the differences larger and thus more manageable. Standard deviation is a great way to get a sense of the variability of the data. Common examples of measures of statistical dispersion are the variance. Students analyze the data to make generalizations about the measures of dispersion. Measures of central tendency serves to locate the center of the distribution. Pdf comparative study of various measures of dispersion david.
Measures of statistical dispersion based on shannon and fisher information concepts lubomir kostal, petr lansky, and ondrej pokora institute of physiology of the czech academy of sciences, videnska 1083, 14220 prague 4, czech republic we propose and discuss two informationbased measures of statistical dispersion of positive continuous ran. Measures of dispersion 4 significance of measuring dispersion to determine the reliability of an average. This paper deals with aggregation types of corporate information security maturity levels from different assets in order to find out how the. In certain types of problems like quality control, weather forecasts, share price. Measures of dispersion definition measures of dispersion. The measure of skewness is how symmetrical or not the distribution of. Characteristics of a good measure of dispersion an ideal measure of dispersion is expected to possess the following properties 1. They include the range, interquartile range, standard deviation and variance. Those measures of dispersion whose units are same as the units of the given series is known as the absolute measure of dispersion. The measure which expresses the variations in terms of the average of deviations of observations like mean deviation and standard deviation. Statistics measures of central tendency and dispersion class 2 session 2 oscarbarrera oscardavid. Measures of central tendency tell you the value that the typical case in the distribution has for your variable.
Lets look at the first of the relative measures of dispersion. Measures of ccentral tendency and dispersion pdf free download important term and concepts. Psychologist stanley smith stevens developed the bestknown classification with four levels, or scales, of measurement. An absolute measure of dispersion contains the same unit as the original data set. The bitrates must be low enough to ensure that pulses are farther apart and therefore the greater dispersion can be tolerated. In this article, we will consider measures of dispersion, which describe how the data is dispersed around a central value. May 31, 20 the sentence what is dispersion measure. Select an appropriate measure of dispersion and correctly calculate.
Measures of dispersion describe the spread of the data. What is the best method for measuring dispersionspread. Most often, chromatic dispersion refers to bulk material dispersion, that is, the change in refractive index with optical frequency. The first is the absolute measure, which measures the dispersion in the same statistical unit.
Ppt measures of dispersion powerpoint presentation free. It is commonly used as a preliminary indicator of dispersion. To reduce fiber dispersion, new types of fiber were invented, including dispersion shifted fibers itu g. Clearly, the extent of spread or dispersion of the data is different in section a from that of b. For the measures of dispersion considered, we will rely on the mean as the standard measure of central tendency, and we will consider measures for both a population and a sample the calculation of these values differs. Measures of dispersion although the range is easy to compute it is a crude measure of variability. Perhaps one of the most widely used measures of dispersion is standard deviation. Another feature of the observation is how the observations are spread about the center. Note in statistics unlike physics a range is given by two numbers, not. Students learn about different measures of variability and standard deviation. May 03, 2018 as a measure of dispersion, the range gives a lot of information about the data. The dispersion of a data set is the amount of variability seen in that data set. To avoid this sort of confusion, one places the noun in quotes when asking about it. You may notice that all the relative measures of dispersion are called coefficients.
Two data sets can have the same mean but they can be entirely different. In addition to it we should have a measure of scatterness of observations. As a result, any new measure of dispersion from the mean that can be invented must be tested against standard deviation because it is the ultimate measure of dispersion from the mean and the. However, in a waveguide there is also the phenomenon of waveguide dispersion, in which case a waves phase velocity in a structure depends on its frequency simply due to the structures ge. Learn about dispersion and measures of dispersion in statistics here. Measures of dispersion include range, interquartile range, variance, standard deviation and absolute deviation. Descriptive statistics examples, types and definition. Calculate and interpret the following measures of dispersion. In the measure phase of the dmaic process in six sigma, there are many types of statistical parameters that graduates of lean six sigma green belt training or other online six sigma courses should know, including absolute measures of dispersion. The scatterness or variation of observations from their average is called the dispersion. As a consequence of its optical characteristics, the chromatic dispersion of a fiber can be changed by acting on the physical properties of the material.
Lets see some more descriptive statistics examples and definitions for dispersion measures. Types of measures of dispersion 1 absolute measures. Measures of central tendency and dispersion these univariate statistics help describe the distribution of a variable. There are two types of measure of dispersion, which are. Notes on types of measures of dispersion,range, quartile. The last measure of variation about the mean is standard deviation, which is an improvement on variance by giving results which are of the same units as initial. The following are the methods of measuring dispersion. These are also known as coefficient of dispersion these are pure numbers or percentages totally independent of the units of measurements. It is a measure of the proportions of the data set. Range the range is the difference between the highest and lowest values of a dataset. Nominal, ordinal, interval and ratio csc 238 fall 2014 there are four measurement scales or types of data.
Measures of dispersion are descriptive statistics that describe. So in addition to central tendency, we should examine the dispersion of the scores in each group as well. In statistics, dispersion is the extent to which a distribution is stretched or squeezed. In simple terms, it shows how squeezed or scattered the variable is. The measure of location or central tendency is a central value that the data values group around. 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. Those are the kinds of statistics this chapter discusses. For the dataset 4, 6, 9, 3, 7 the lowest value is 3, highest is 9, so the range is 936. The observations may be close to the center or they may be spread away from the center. It shows how much variation from the average exists. We use a relative measure of dispersion for comparing distributions of two or more data set and for unit free comparison. Lesson plan measuring dispersion grade 11 grade 11. The range is given as the smallest and largest observations.
Dispersion measures how the various elements behave with regards to some sort of central tendency, usually the mean. The second type is the relative measure of dispersion, which measures the ratio unit. Learning objectives after completion of this module, the student will be able to calculate central tendencies and measures of dispersion of data sets employing both. In statistics, there are many techniques that are applied to measure dispersion.
It is a value which is typical or representative of a set of data. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. Out of several measures of dispersion, the most frequently used measure is standard deviation. Hence two distribution with different units can be compared with the help of relative measures of dispersion. If the original measurements in sets 1 and 2 were of length in.
Geometric mean and har monic mean, which ar e suitable in certain situations. There are different measures of dispersion like the range, the quartile deviation, the mean deviation and the standard deviation. In the above distribution, the first distribution has zero dispersion, and the second distribution has a dispersion greater than the former. The measure of skewness is how symmetrical or not the distribution of data values is. This averaged deviation or dispersion is nothing else, but the average of the second order. 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. In statistics, the measures of dispersion help to interpret the variability of data i. 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. These are simply ways to categorize different types of variables. Dec 17, 2019 therefore, six sigma practitioners who have got the lean six sigma training or another lean six sigma green belt course will know that six sigma teams are confronted with many different types of data in different units of measure. Although absolute deviation is also a measure of dispersion, variance and standard deviation are better measures because of the way theyre calculated. Sd is the square root of sum of squared deviation from the mean divided by the number of observations.
A statistical measuring the spread or variability of the sample around the mean or in other words it may be defined as the measure of dispersion of different variables around the central value. They each tell you something different about what the distribution looks like. 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. For the study of dispersion, we need some measures which show whether the dispersion is small or large. Statistics measures of central tendency and dispersion. The measures of dispersion you have just seen differ in ways that will help determine which one is most useful in a particular situation. Central tendency and dispersion sage publications inc. They are the coefficient of range, the coefficient of mean deviation, the coefficient of quartile deviation, the coefficient of variation, and the coefficient of standard deviation. Measures of central tendency and dispersion paris school of.
May 06, 2017 definition of measure of dispersion in statistics, dispersion also called variability, scatter, or spread is the extent to which a distribution is stretched or squeezed. As a result, any new measure of dispersion from the mean that can be invented must be tested against standard deviation because it is the ultimate measure of dispersion. Measures of location and dispersion and their appropriate. The one issue with sample variance is it is in squared units, not the original unit of measurement. Jun 11, 2009 in statistics, dispersion has two measure types. Relative measures are not expressed in units but it is a pure number. The measure of dispersion shows how the data is spread or scattered around the mean. So the two mean deviations computed above indicate almost similar dispersion. Of all the measures of dispersion, the range is the easiest to determine. Thus to describe data, one needs to know the extent of variability.
Dispersion limits the bandwidth or information carrying capacity of a fiber. Range, interquartile range, and standard deviation. Coefficient of standard deviation the standard deviation is the absolute measure of dispersion. Measures of statistical dispersion based on shannon and. It mentions the minimum and maximum values as the extremes, and.
Ppt measures of dispersion powerpoint presentation. Most measures of dispersion have the same units as the quantity being measured. When describing the scores on a single variable, it is customary to report on both the central. Know what is dispersion, types and formulas of dispersion methods along with example.
They learn that the standard deviation is an accepted statistic to measure the dispersion of data about the mean. Relative measures of dispersion are measures of the variance of a range of values regardless of its unit of measure. The measures of central tendency are not adequate to describe data. This formula is a definitional one and for calculations, an easier formula is used. 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. In this lesson, you will read about the following measures of dispersion. Understanding measures of dispersion in statistics. 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. There are two main types of dispersion methods in statistics which are.
As with other types of measures, there is more than one approach to defining such a measure. The units for the dispersion coefficient are practical units more relevant to the long lengths of fibers used in telecommunication applications. We will only discuss three of the four relative measures of dispersion in this article. These types of dispersions can be used only in the comparing the variability of the series or distribution having the same units. A free powerpoint ppt presentation displayed as a flash slide show on id. Measures of dispersion explained magoosh statistics blog. There are three main measures of variation, the range, the variance and the standard deviation. A measure of dispersion is capable of algebraic treatment. In other words, if the measurements are in metres or seconds, so is the measure of dispersion.
The range of a set of data is the largest measurement minus the smallest measurement. The range is simply the largest observation minus the smallest observation. The spss guide contains only the briefest discussion of measures of dispersion on pages 2324. The word dispersion has a technical meaning in statistics. They derive a formula for finding standard deviation of data sets. Standard deviation sd is the most commonly used measure of dispersion. Absolute measures of dispersion are expressed in the unit of variable itself. The dispersion measure, dm, is simply a constant of proportionality relating the frequency of the light to the extra amount of time relative to vacuum required to reach the observer due to dispersion.
38 667 564 1181 1263 1467 694 210 1262 340 312 197 1387 329 66 854 831 670 913 40 211 1348 725 1316 859 738 1403 702 364 1475 538 1386