There are different measures of dispersion like the range, the quartile deviation, the mean deviation and the standard deviation. Measures of dispersion include range, interquartile range, variance, standard deviation and absolute deviation. 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. In finance, dispersion is used in studying the effects of investor and analyst. Measures of central tendency help us to represent the entire mass of the data by a single value. Put a vertical line at the median, across the interior of the rectangle. To facilitate the use of other statistical measures. In simple terms, it shows how squeezed or scattered the variable is. The difference between the smallest and largest values in the data set. Consider the following two sets of data which have the same mean, 25, and the same range. There are two main types of dispersion methods in statistics which are. Method validation and comparisons with some most important tools of dispersion measures e.
The observations may be close to the center or they may be spread away from the center. In statistics, dispersion also called variability, scatter, or spread is the extent to which a distribution is stretched or squeezed. How to calculate the measures of central tendency and dispersion for a grouped frequency distribution 4 2 the median. Dispersion is contrasted with location or central tendency, and. Characteristics of a good measure of dispersion an ideal measure of dispersion is expected to possess the following properties 1. Dispersion measures how the various elements behave with regards to some sort of central tendency, usually the mean. The average measures the center of the data, and it is one aspect of observation. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. Measures of dispersion range, variance standard deviation coefficient of variation computation of the above statistics for raw and grouped data measures of dispersion the averages are representatives of a frequency distribution. Measures of dispersion 4 significance of measuring dispersion to determine the reliability of an average.
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 central tendency are called averages of first order, but these are not sensitive to the variability among the data. Lets have a detailed look at absolute measures of dispersion and how they are used in six sigma practices. Two data sets can have the same mean but they can be entirely different. Central tendency gets at the typical score on the variable, while dispersion gets at how much variety there is in the scores.
In 4, 6, 9, 3, 7 the lowest value is 3, and the highest is 9. If the observations of an ungrouped data are arranged in increasing or decreasing order of their magnitude, a value which divides these ordered observations into two equal parts is called the median of the data. Ppt measures of dispersion powerpoint presentation. Construct a rectangle with one end at the first quartile and the other end at the third quartile. Calculate the mean and the range of each of the following sets of data. Dispersion measures of variability introduction and definition. There are various types of measures of dispersion like range, mean deviation. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.
Thus to describe data, one needs to know the extent of variability. Measures of dispersion although the range is easy to compute it is a crude measure of variability. The median of any data set is the middle value when the measurements are arranged in ascending or descending order. Dispersion is a statistical term describing the size of the range of values expected for a particular variable. The measures of central tendency are not adequate to describe data. Unitii measures of central tendency and dispersion. In statistics, the measures of dispersion help to interpret the variability of data i. Pdf on oct 1, 2011, s manikandan and others published measures of dispersion find, read and cite all the research you need on researchgate. Ncert solution for class 11 statistics chapter 6 measures.
In lesson 2, you learned about frequency distributions, ratios, proportions, and rates. 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. Such a number is called a measure of central tendency. Lesson 3 measures of central location and dispersion as epidemiologists, we use a variety of methods to summarize data. The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. These types of dispersions can be used only in the comparing the variability of the. Measuring market opportunity december 20 index investment strategy 2 the result is sometimes called crosssectional portfolio volatility. Notes of ecco measures of dispersion for class 11 chapter 6 download pdf.
Measures of dispersion are descriptive statistics that describe. A large measure of dispersion indicates that the mean is not reliable it is not representative of the data. Notes of ecco measures of dispersion for class 11 download pdf. There are three main measures of variation, the range, the variance and the standard deviation. The first is the absolute measure, which measures the dispersion in the same statistical unit. Locate smallest and largest values within the intervals fl. Dispersion is a general term for different statistics that describe how values are distributed around the centre. Cbse economics chapter 6 measures of dispersion class 11 notes economics in pdf are available for free download in mycbseguide mobile app. Statistics measures of central tendency and dispersion class 2 session 2 oscarbarrera oscardavid. For the measures of dispersion considered, we will rely on the mean as the standard measure of central tendency, and we will. Measures of central tendency and dispersion paris school of.
Range the difference between the maximum and minimum values on the scale of measurement. Measures of dispersion range, variance standard deviation co efficient of variation computation of the above statistics for raw and grouped data. The measure of dispersion indicates the degree of spread or distribution of the data. Those measures of dispersion whose units are same as the units of the given series is known as the absolute measure of dispersion. The word dispersion has a technical meaning in statistics.
Ncert solution for class 11 statistics chapter 6 measures of dispersion covers all the questions provided in ncert books for 11th class statistics subject. In this section we will look at measures of dispersion. 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. In analyzing, statistical data, it is often useful to have numbers describe the complete set of data. What is the best method for measuring dispersionspread. The range of a data set is the difference between the maximum and minimum values in the set. Measure of central tendency give us good information about the scores in our. In statistics, there are many techniques that are applied to measure dispersion. This is only used for ordinal and interval scale data. The most straightforward measure of dispersion is the range. In this lecture we will cover the three basic measures of dispersion. Example calculate the range for the data for quarterback a and quarterback b in the example above. The more similar the scores are to each other, the lower the measure of.
The population variance is the squared value of the population standard deviation. 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. Two distributions may have same mean, median and mode but the variability among the data in two distributions may be quiet different. The second type is the relative measure of dispersion, which measures the ratio unit. 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. Measures of dispersion 29 measures of dispersion you have learnt various measures of central tendency.
Statistics measures of central tendency and dispersion. Dispersion refers to the variation of the items around an average. Graphs and statistics central tendency and dispersion. The range of a set of data is the largest measurement minus the smallest measurement. In this article, we will consider measures of dispersion, which describe how the data is dispersed around a central value. For standard deviation, the deviations are first squared and averaged and then square root of the average is found.
Measures of dispersion, also known as variation, tell us how spread out or compact the data tends to be. The dispersion of a data set is the amount of variability seen in that data set. The population standard deviation shows how far away each value is from the mean on average. When describing the scores on a single variable, it is customary to report on both the central tendency. Mean deviation tries to overcome this problem by ignoring the signs of deviations, i. Understanding measures of dispersion in statistics.
Measures of dispersion range, variance standard deviation coefficient of variation computation of the above statistics for raw and grouped data. The measures which express the scattering of observation in terms of distances i. 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. The measure which expresses the variations in terms of the average of deviations of observations like mean deviation and standard deviation. Practics question for ch 10 measures of dispersion exercise 1p 268.
Measures of central tendency are used because they represent centralized or middle values of the data. Central tendencyvariability measures of central tendency. Those are the kinds of statistics this chapter discusses. The minimum number of completions for quarterback a is 19, the maximum is 37. Types of measures of dispersion,range, quartile deviation. Measures of statistical dispersion wyzant resources.
Measures of dispersion are closely related to measures of central tendency. Lesson initiator what is the purpose of finding an average. Brief discussions and associated formulas for measures of central tendency, dispersion, and variation in data sets. Another feature of the observation is how the observations are spread about the center. The range is simply the largest observation minus the smallest observation. 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. Can the central tendency describe the data fully and adequately.
Measure of dispersion an overview sciencedirect topics. This gives a measure of the spread of values but no indication of how they are distributed. Pdf comparative study of various measures of dispersion david. Compute for the interquartile range, lower fence, and upper fence. Calculate the different measures of variability of a given ungrouped data. Lesson 5 measures of dispersion outline measures of dispersion. Should take individual values from the distribution into account so no value is left out. Measures of dispersion are the statistical formula to measure the spread of the. A free powerpoint ppt presentation displayed as a flash slide show on id. But they fail to give a complete picture of the distribution.
1012 1422 718 516 414 1396 793 319 535 1457 597 48 621 1288 547 1413 664 1328 766 1105 1243 782 818 500 1483 992 263 1317 391 1427 924 1180 1092