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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.
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What is despersion?
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.
What important feature of the data set is not revealed through the different measures of centre?
The dispersion of the data.
Why measures of dispersion are important along with measures of central tendency to understand the nature 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.
Dispersion is the degree of variation in the data?
No
What are descriptive statistics used to describe?
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.
What is despersion?
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.
What important feature of the data set is not revealed through the different measures of centre?
The dispersion of the data.
Which measures of central tendency become larger as the data is more dispersed?
None. Measures of central tendency are not significantly affected by the spread or dispersion of data.
What is a number that helps describe all of the data in a data set?
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.
Why measures of dispersion are important along with measures of central tendency to understand the nature 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.
What are the units of dispersion?
The units of dispersion are dependent on the units of the data being measured. Common measures of dispersion include variance and standard deviation, which have square units and the same units as the data being measured, respectively. Another measure, such as the coefficient of variation, is a unitless measure of dispersion relative to the mean.
How can you describe variation in a set of data?
measures of variation
What is relative measure?
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)
How do we obtain useful information from a set of data?
You calculate summary statistics: measures of the central tendency and dispersion (spread). The precise statistics would depend on the nature of the data set.
What is used to describe a set of data where the measures cluster or concentrate at a point?
The answer depends on the type of distribution for the data. It could be the modal class.
Dispersion is the degree of variation in the data?
No
What are descriptive statistics used to describe?
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.
