advantages and disadvantages of measures of dispersion

Common-sense would suggest dividing by n, but it turns out that this actually gives an estimate of the population variance, which is too small. WebAdvantages and disadvantages of the mean and median. This new, advert-free website is still under development and there may be some issues accessing content. Websures of dispersion. WebThe product has the characteristics of fine particle size, narrow particle size distribution, smooth particle surface, regular particle shape, high purity, high activity, good dispersion, and low temperature rise in crushing; the disadvantages are high equipment manufacturing costs, large one-time investment, and high energy consumption. It holds for a large number of measurements commonly made in medicine. However, the interquartile range and standard deviation have the following key difference: The interquartile range (IQR) is not affected by extreme outliers. As stated above, the range is calculated by subtracting the smallest value in the data set from the largest value in the data set. You may however be asked to interpret a standard deviation value (explain to the examiner what the measure means). One of the simplest measures of variability to calculate. The calculations required to determine the sum of the squared differences from the mean are given in Table 1, below. The well-known statistical device to exhibit this kind of a ground level reality is to trace out a Lorenz-Curve, also called the Curve of Concentration and measure the exact nature and degree of economic inequality existing among the weavers of Nadia with the aid of GINI- COEFFICIENT, an unit free positive fraction (lying in between 0 and 1). Consider below Data and find out if there is any OutLiers . It is thus known as the Curve of Concentration. We use these values to compare how close other data values are to them. This website uses cookies to improve your experience while you navigate through the website. So we need not know the details of the series to calculate the range. Web2. This will always be the case: the positive deviations from the mean cancel the negative ones. Cookie Policy - Terms and Conditions - Privacy Policy, AP Statistics: Percentiles, Quartiles, z-Scores (measures of position). Due to the possibility that (on occasion) measures of central tendency wont be the best way for a number to represent a whole data set, it is important to present a measure of dispersion alongside a measure of central tendency. WebThe disadvantages of mean, mode, and median are the same as their advantages: they are simple, not sophisticated enough to use when comparing data sets. But opting out of some of these cookies may affect your browsing experience. (c) It is rarely used in practical purposes. The statisticians here prescribe for an well-known concept dispersion or the scatteredness or variability of the values of the variable usually from their arithmetic mean. The main disadvantage of the mean is that it is vulnerable to outliers. (i) Calculate mean deviation about Arithmetic Mean of the following numbers: Let us arrange the numbers in an increasing order as 15, 30, 35, 50, 70, 75 and compute their AM as: AM = 15 + 30 + 35 + 50 + 70 + 75/6 = 275/6. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively. The main disadvantage of the mean is that it is vulnerable to outliers. Range as a measure of the variability of the values of a variable, is not widely accepted and spontaneously prescribed by the Statisticians of today However, it is not totally rejected even today as it has certain traditional accept abilities like representing temperate variations in a day by recording the maximum and the minimum values regularly by the weather department, while imposing controlling measures against wide fluctuations in the market prices of the essential goods and services bought and sold by the common people while imposing Price-control and Rationing measures through Public Sector Regulations, mainly to protect interests of both the buyers and sellers simultaneously. Here lies the superiority of the Relative Measures over the Absolute Measures of dispersion. TOS4. It is estimated by first ordering the data from smallest to largest, and then counting upwards for half the observations. By clicking Accept, you consent to the use of ALL the cookies. Therefore, the SD possesses almost all the prerequisites of a good measure of dispersion and hence it has become the most familiar, important and widely used device for measuring dispersion for a set of values on a given variable. If outliers are present it may give a distorted impression of the variability of the data, since only two observations are included in the estimate. Measures of dispersion describe the spread of the data. x1 = x2 = x3 = xn), then they would equal the mean, and so s would be zero. Disadvantages of Coefficient of Variation 1. Toggle Advantages and disadvantages subsection 5.1 Advantages. According to them, it should be based on all the given observations, should be readily comprehensible, fairly and easily calculable, be affected as little as possible by sampling fluctuations and amenable to further algebraic treatments. While computing the result it involves larger information than the Range. WebClassification of Measures of Dispersion. Central tendency gets at the typical score on the variable, while dispersion gets at how much variety there is in the scores. This process is demonstrated in Example 2, below. The deviation from the mean is determined by subtracting the mean from the data value. (a) Quartile Deviation is easy to calculate numerically. Question. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. (g) Statisticians very often prescribe SD as the true measure of dispersion of a series of information. 2. Using other methods of dispersion, such as measuring the interquartile range, the difference between the 25th and 75th percentile, provide a better representation of dispersion in cases where outliers are involved. (1) It requires the mean to be the measure of central tendency and therefore, it can only be used with interval data, because ordinal and nominal data does not have a mean. Calculate the Mean Deviation for the following data: To calculate MD of the given distribution, we construct the following table: While studying the variability of the observations of a variable, we usually use the absolute measures of dispersion namely the Range, Quartile deviation. They are liable to yield inappropriate results as there are different methods of calculating the dispersions. (c) The definition and the concept of dispersion should be complete and comprehensive enough. This is a weakness as it can be argued that the range is not always a representative description of the spread of a set of data. It will enable us to avoid mistakes in calculation and give us the best result. (b) It can also be calculated about the median value of those observations as their central value and then it gives us the minimum value for the MD. Consider the following three datasets:(1) 5, 25, 25, 25, 25, 25, 45(2) 5, 15, 20, 25, 30, 35, 45(3) 5, 5, 5, 25, 45, 45, 45. Moreover, biofilms are highly So the degree of population remains N only. It is the most popular central tendency as it is easy to understand. Exam Tip:Be careful when reading tables that have a SD. 1. In order to get the df for the estimate, you have to subtract 1 from the number of items. The following are thus unhesitatingly considered as important characteristics for an ideal measure of dispersion: (b) It should be easy to calculate and easily understandable. For example, if we had entered '21' instead of '2.1' in the calculation of the mean in Example 1, we would find the mean changed from 1.50kg to 7.98kg. (c) It should be calculated considering all the available observations. Defined as the difference For example, if one were to measure a students consistency on quizzes, and he scored {40, 90, 91, 93, 95, 100} on six different quizzes, the range would be 60 points, marking considerable inconsistency. (d) It is easily usable and capable of further Mathematical treatments. WebMerits of Mean: 1. For some data it is very useful, because one would want to know these numbers, for example knowing in a sample the ages of youngest and oldest participant. This method results in the creation of small nanoparticles from bulk material. Let us now look at some advantages and disadvantages of this measure: Advantages: Based on all observations; Doesnt change with change in origin; Next add each of the n squared differences. WebIntroductory statistics - Assignment 2: List the advantages and disadvantages of Measures of Central - Studocu Solved business statistics assignment questions assignment list the advantages and disadvantages of measures of central tendency vis vis measures of dispersion DismissTry Ask an Expert Ask an Expert Sign inRegister Sign inRegister Home The It is easy to calculate. This method results in the creation of small nanoparticles from bulk material. This is one of the constraint we have on any sample data. This is a strength as this speeds up data analysis allowing psychologists and researchers to draw conclusions about their research at a faster pace. What is range merit and disadvantage? (c) It can be used safely as a suitable measure of dispersion at all situations. Standard deviation and average deviation are also commonly used methods to determine the dispersion of data. But, the results of such measures are obtained in terms of the units in which the observations are available and hence they are not comparable with each other. It can be found by mere inspection. Huang et al. Bacteria in the human body are often found embedded in a dense 3D structure, the biofilm, which makes their eradication even more challenging. Laser diffraction advantages include: An absolute method grounded in fundamental scientific principles. If the skewness is between -0.5 and 0.5, the data are fairly symmetrical. For the data presented with their respective frequencies, the idea is to measure the same as the difference between the mid-values of the two marginal classes. It is to be noted that any change in marginal values or the classes of the variable in the series given will change both the absolute and the percentage values of the Range. (b) It uses AM of the given data as an important component which is simply computable. What are the advantages and disadvantages of arithmetic mean? However, there is an increasingly new trend in which very few people are retiring early, and that too at very young ages. Disadvantage 2: Not suitable for time series They indicate the dispersal character of a statistical series. One drawback to variance is that it gives added weight to outliers, the numbers that are far from the mean. The range is given as the smallest and largest observations. Skew. a. Statisticians use variance to see how individual numbers relate to each other within a data set, rather than using broader mathematical techniques such as arranging numbers into quartiles. 3. WebAssignment 2: List the advantages and disadvantages of Measures of Central Tendency vis a vis Measures of Dispersion. We can represent AM of the given number as: Now, we calculate the desired SD through the following exercise: Find the SD for the following distribution: To calculate SD of the given distribution, we reconstruct the following table: 4. The major advantage of the mean is that it uses all the data values, and is, in a statistical sense, efficient. We found the mean to be 1.5kg. However, it is not statistically efficient, as it does not make use of all the individual data values. It does not store any personal data. The prime advantage of this measure of dispersion is that it is easy to calculate. For determining the proportionate Quartile Deviation, also called the Coefficient of Quartile Deviation, we use the following formula: Calculate the Quartile Deviation and Co-efficient of Quartile Deviation from the following data: Here, n = 7, the first and third quartiles are: Determine the QD and CQD from the following grouped data: In order to determine the values of QD and Co-efficient of QD Let us prepare the following table: Grouped frequency distribution of X with corresponding cumulative frequencies (F). The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. Share Your Word File The interquartile range is a useful measure of variability and is given by the lower and upper quartiles. The lower dispersion value shows the data points will be grouped nearer to the center. The mean of data set A is46. 32,980,12567,33000,99000,545,1256,9898,12568,32984, Step 1: We arrange these observations in ascending order. Like the measures of central tendency, most of the measures of dispersion do not give a convincing idea about a series to a layman. They are liable to misinterpretations, and wrong generalizations by a statistician of based character. Further algebraic treatments can also be applied easily with the result obtained afterwards. All rights reserved. They enable the statisticians for making a comparison between two or more statistical series with regard to the character of their stability or consistency. This will make the tail of the distribution longer towards the left side or the lower side, and the less values (low ages) will shift the mean towards the left, making it a negatively skewed distribution. It is measured as= (highest value lowest value) of the variable. The range is the difference Characteristics of an ideal measure of dispersion:- The characterstics for an ideal measure of This is important to know the spread of your data when describing your data set. You also have the option to opt-out of these cookies. WebBacterial infections are a growing concern to the health care systems. It is not affected by sampling so that the result is reliable. The median is the average of the 9th and 10th observations (2.18+2.22)/2 = 2.20 kg. Necessary cookies are absolutely essential for the website to function properly. However, a couple of individuals may have a very high income, in millions. Advantage 1: Fast and easy to calculate. This cookie is set by GDPR Cookie Consent plugin. Quartile Deviation: While measuring the degree of variability of a variable Quartile Deviation is claimed to be another useful device and an improved one in the sense it gives equal importance or weightage to all the observations of the variable. They include the range, interquartile range, standard deviation and variance. Divide the sum in #4 by (n 1). The locus that we have traced out here as O-A-B-C-D-E-0 is called the LORENZ-CURVE.