# Uses of measures of dispersion. Measures of Dispersion 2022-10-14

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Measures of dispersion are statistical tools used to describe the spread or variability of a set of data. They provide a way to quantify how far apart the individual data points are from each other and from the mean or average value of the data set. There are several different measures of dispersion, including range, interquartile range, variance, and standard deviation. Each of these measures has specific uses and can be helpful in different contexts.

One common use of measures of dispersion is to understand the distribution of values within a data set. For example, if a data set contains scores on a test, the mean or average score can give us a general idea of how well the students did overall. However, the mean alone does not tell us anything about how widely the scores were dispersed. Were all the scores relatively close to the mean, or were there some scores that were much higher or lower than the average? Using a measure of dispersion can help us understand the spread of the scores and give us a more complete picture of the data.

Measures of dispersion can also be useful in comparing different data sets. For example, if we have data on the test scores of two different classes, we might want to know which class performed better overall. Simply comparing the mean scores of the two classes could be misleading if the scores in one class are more dispersed than in the other. In this case, using a measure of dispersion can help us account for the spread of the scores and make a more accurate comparison.

Another use of measures of dispersion is in determining the sample size needed for a study. In some cases, a larger sample size may be needed if the data are more dispersed, as a larger sample will be needed to accurately represent the spread of the data. On the other hand, a smaller sample size may be sufficient if the data are more concentrated around the mean.

Finally, measures of dispersion can be used in statistical analysis to help identify patterns or trends in the data. For example, if we are studying the relationship between two variables, we might want to know if there is a strong correlation between the variables or if the relationship is more scattered. Measures of dispersion can help us understand the spread of the data and whether there is a clear trend or pattern.

In summary, measures of dispersion are useful tools for understanding the spread or variability of a data set. They can be used to compare different data sets, determine sample size, and identify patterns or trends in the data. By quantifying the dispersion of a data set, we can gain a more complete and accurate understanding of the data.

## Measures of dispersion

Why are measures of dispersion important in statistics? It is affected very greatly by fluctuations in sampling. We will follow with a step-by-step example to illustrate how to calculate the standard deviation. For more details, please refer to the CSM®, CSPO®, CSD®, CSP®, A-CSPO®, A-CSM® are registered trademarks of Scrum Alliance®. In particular, if the standard deviation is of a similar size to the mean, then the SD is not an informative summary measure, save to indicate that the data are skewed. Disadvantages: a Quartile deviation as a measure of disper­sion is not much popularly prescribed by the statisticians. Let us analyse this phenomenon in terms of a study based on the distribution of personal incomes of the chosen sample respondents that is how the total income of the entire workforce is shared by the different income classes.

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## 4 Commonly Used Measures of Dispersion

Yule and Kendall is well accepted, complete and comprehensive in nature as it includes all the important characteristics for an ideal measure of dispersion. Usually, the deviation is taken from the mean of the distribution. It is not used much in statistical analysis, since its value depends on the accuracy with which the data are measured; although it may be useful for categorical data to describe the most frequent category. How measure of central tendency and measure of dispersion can complement each other to understand a distribution? Before measuring the data, it is important to understand the diversion of the terms and variations. Absolute Measures of Dispersion: 1. In the two examples, we have: In the first case, mean deviation is almost 25% of the mean, while in the second case it is less.

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## Measures of Dispersion: Definition & Examples, Psychology

D : The required standard deviation is 2. And the SD is the most sensitive measure of dispersion as all values in the data set are considered. In other words the average of the deviations of all the values from the arithmetic mean is known as mean deviation or average deviation. It explains the disparity of data from one another, delivering a precise view of their distribution. Dispersion is the degree to which data is distributed around this central tendency, and is represented by range, deviation, variance, standard deviation and standard error. As you work through this series of short, engaging and informative lessons, you'll become familiar with topics like range, standard deviation, variance, z-scores and dispersion.

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## Measures of Dispersion in Business

In other words, it is a point below which 50% of the scores lie. The example highlights the practicality of the measures of dispersion and how it can help a researcher understand more about their findings. Lower spread means better yield, and a higher spread represents lower yield. Range as compared above is in a crude form or is an absolute measure of dispersion and is unfit for the purposes of comparison, especially when the series are in two different units. The standard deviation is vulnerable to outliers, so if the 2. The squared deviations used in computing SD are always taken from the mean, never from the median or mode. Dispersion is said to be significant when variation or lack of uniformity in the size of items of a series is great aid substantial.

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## What are the significance of measures of dispersion?

Absolute and Relative Measures: 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 second quartile, or 5th decile or the 50th percentile is the median see Figure. Outliers are single observations which, if excluded from the calculations, have noticeable influence on the results. Moreover, the normal curve is directly related to S. It is defensible when used with ratio scales—scales in which the units are equal and there is a true zero or reference point.

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## Dispersion in Statistics

For these limitations, the method is not widely accepted and applied in all cases. In other words, the IQR is the first quartile subtracted from the third quartile. ADVERTISEMENTS: Advantages : 1. You'll say: 'Well, most people are 18, a few in their 20s and two or three over 40. The chapter also shows you how these measures of dispersion can be applied in business contexts. What is the difference between central tendency measures and measures of dispersion? The average wage might be the same, but the variation or dispersion of the wages might be very different. For instance, in At the same time, it allows investors to estimate the statistical distribution of potential Portfolio Returns The portfolio return formula calculates the return of the total portfolio consisting of the different individual assets.

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## Measures of Dispersion in Statistics (Definition & Types)

This single value helps us in making comparisons of various distributions. The study of variation may also be looked upon as a means of determining uniformity or consistency. Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data. Co-efficient of Mean Deviation : The co-efficient of Mean Deviation can be computed using the mean or median of the data. However, the rest of the dispersion measures are totally different as measured by the above methods.

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## Measures of Location and Dispersion and their appropriate uses

As in the case of mean deviation, the interpretation of standard deviation requires the value of M and N for consideration. When it is desired to weigh all the deviations according to their size. The usual Relative Measures of Dispersion are: Among these four coefficients stated above the Coefficient of Variation is widely accepted and used in almost all practical situations mainly because of its accuracy and hence its approximation to explain the reality. Here, the signs of deviations are not disregarded, instead they are eliminated by squaring each of the deviations. For example a test results 20 scores and these scores are arranged in a descending order. The higher the value of the range, the higher the spread in data.

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