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Sets of data have many characteristics. The central location (mean, median) is one measure. But you can have different data sets with the same mean. So a measure of dispersion is used to determine whether there is a little or a lot of variability within the set. Sometimes it is necessary to look at higher order measures like the skewness, kurtosis.

Q: Why are the measures of dispersion necessary to describe a set of data?

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Dispersion is an abstract quality of a sample of data. Dispersion is how far apart or scattered the data values appear to be. Common measures of dispersion are the data range and standard deviation.

The dispersion of the data.

Central tendency will only give you information on the location of the data. You also need dispersion to define the spread of the data. In addition, shape should also be part of the defining criteria of data. So, you need: location, spread & shape as best measures to define data.

No

They describe the basic features of data. They provide summaries about the sample and the measures, and together with simple graphic analysis, they form the basis of virtually every analysis of data.

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Dispersion is an abstract quality of a sample of data. Dispersion is how far apart or scattered the data values appear to be. Common measures of dispersion are the data range and standard deviation.

The dispersion of the data.

None. Measures of central tendency are not significantly affected by the spread or dispersion of data.

There is no single number. There are several different measures of central tendency - different ones are better in different circumstances. Then there are several measures of spread or dispersion, skewness and so on. All of these are characteristics of the data and they cannot all be summarised by a single number.

Central tendency will only give you information on the location of the data. You also need dispersion to define the spread of the data. In addition, shape should also be part of the defining criteria of data. So, you need: location, spread & shape as best measures to define data.

measures of variation

These measures are calculated for the comparison of dispersion in two or more than two sets of observations. These measures are free of the units in which the original data is measured. If the original data is in dollar or kilometers, we do not use these units with relative measure of dispersion. These measures are a sort of ratio and are called coefficients. Each absolute measure of dispersion can be converted into its relative measure. Thus the relative measures of dispersion are:Coefficient of Range or Coefficient of Dispersion.Coefficient of Quartile Deviation or Quartile Coefficient of Dispersion.Coefficient of Mean Deviation or Mean Deviation of Dispersion.Coefficient of Standard Deviation or Standard Coefficient of Dispersion.Coefficient of Variation (a special case of Standard Coefficient of Dispersion)

You calculate summary statistics: measures of the central tendency and dispersion (spread). The precise statistics would depend on the nature of the data set.

The answer depends on the type of distribution for the data. It could be the modal class.

No

They describe the basic features of data. They provide summaries about the sample and the measures, and together with simple graphic analysis, they form the basis of virtually every analysis of data.

It's a statistical tool used in psychology. A simple way of calculating the measure of dispersion is to calculate the range. The range is the difference between the smallest and largest value in a set of scores. This is a fairly crude measure of dispersion as any one high or low scale can distort the data. A more sophisticated measure of dispersion is the standard deviation which tells you how much on average scores differ from the mean.