Which measure of dispersion is useful in comparing the variabilities of two or more sets of data with different means and units?
Question: Which measure of dispersion is useful in comparing the variabilities of two or more sets of data with different means and units?
The best measure of dispersion to compare the variabilities of two or more sets of data with different means and units is the coefficient of variation (CV).
The CV is calculated by dividing the standard deviation by the mean and multiplying by 100%. It is expressed as a percentage, which makes it easy to compare the variabilities of different sets of data.
For example, consider two sets of data with the following means and standard deviations:
| Set | Mean | Standard Deviation | CV |
|---|---|---|---|
| A | 100 | 10 | 10% |
| B | 200 | 20 | 10% |
Even though the standard deviations of the two sets of data are the same, the CV shows that they have the same variability. This is because the standard deviation of Set B is twice as large as the standard deviation of Set A, but the mean of Set B is also twice as large as the mean of Set A.
The CV can be used to compare the variability of any two or more sets of data, regardless of the units of measurement. This makes it a very versatile measure of dispersion.
Here are some examples of how the CV can be used:
- To compare the variability of student test scores in different schools.
- To compare the variability of product quality in different factories.
- To compare the variability of employee salaries in different companies.
The CV is a valuable tool for comparing the variabilities of different sets of data, and it is widely used in a variety of fields.
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