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What is the relative dispersion with the mean of 45000 and a standard deviation of 9000?
Relative dispersion = coefficient of variation = (9000/45000)(100) = 20.
What are the criteria for choosing measure of central tendency and measure of variation?
Central tendency is measured by using the mean, median and mode of a set of numbers. Variation is measured by using the range, variance and standard deviation of a set of numbers.
Why are the measures of dispersion necessary to describe a set of data?
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.
Does standard deviation and mean deviation measure dispersion the same?
No. The average of the deviations, or mean deviation, will always be zero. The standard deviation is the average squared deviation which is usually non-zero.
What does one standard deviation mean?
Standard deviation is a measure of variation from the mean of a data set. 1 standard deviation from the mean (which is usually + and - from mean) contains 68% of the data.
