Q: Why standard deviation is the best measurement for dispersion?

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The standard deviation of the population. the standard deviation of the population.

There is 1) standard deviation, 2) mean deviation and 3) mean absolute deviation. The standard deviation is calculated most of the time. If our objective is to estimate the variance of the overall population from a representative random sample, then it has been shown theoretically that the standard deviation is the best estimate (most efficient). The mean deviation is calculated by first calculating the mean of the data and then calculating the deviation (value - mean) for each value. If we then sum these deviations, we calculate the mean deviation which will always be zero. So this statistic has little value. The individual deviations may however be of interest. See related link. To obtain the means absolute deviation (MAD), we sum the absolute value of the individual deviations. We will obtain a value that is similar to the standard deviation, a measure of dispersal of the data values. The MAD may be transformed to a standard deviation, if the distribution is known. The MAD has been shown to be less efficient in estimating the standard deviation, but a more robust estimator (not as influenced by erroneous data) as the standard deviation. See related link. Most of the time we use the standard deviation to provide the best estimate of the variance of the population.

Few ancient measurements were 'standard'. Generally two people doing business agreed on the standard between them. A cubit was a body-based measurement - supposedly the length of a forearm. To the best of my knowledge, only the 'carob' was a standard measurment - as the seeds of the carob are, apparently, always the same weight.

Measurement error: obviously!

The answer depends on the purpose. The interquartile range and the median absolute deviation are both measures of spread. The IQR is quick and easy to find whereas the MAD is not.

Related questions

standard deviation is best measure of dispersion because all the data distributions are nearer to the normal distribution.

No. A small standard deviation with a large mean will yield points further from the mean than a large standard deviation of a small mean. Standard deviation is best thought of as spread or dispersion.

standard deviation is the best measure of dispersion because.. a)It measure the absolute dispersion b)It is most frequentlyused as prossesses almost all the the qualities that a good measure of variation have. c)It is beased on all observation. d)It is rigidly defined. e)It is capable of further algebraic treatment. f)It is least affected by the fluctuation of sampling.

The standard deviation of the population. the standard deviation of the population.

There is 1) standard deviation, 2) mean deviation and 3) mean absolute deviation. The standard deviation is calculated most of the time. If our objective is to estimate the variance of the overall population from a representative random sample, then it has been shown theoretically that the standard deviation is the best estimate (most efficient). The mean deviation is calculated by first calculating the mean of the data and then calculating the deviation (value - mean) for each value. If we then sum these deviations, we calculate the mean deviation which will always be zero. So this statistic has little value. The individual deviations may however be of interest. See related link. To obtain the means absolute deviation (MAD), we sum the absolute value of the individual deviations. We will obtain a value that is similar to the standard deviation, a measure of dispersal of the data values. The MAD may be transformed to a standard deviation, if the distribution is known. The MAD has been shown to be less efficient in estimating the standard deviation, but a more robust estimator (not as influenced by erroneous data) as the standard deviation. See related link. Most of the time we use the standard deviation to provide the best estimate of the variance of the population.

Standard deviation; correlation coefficient

The best measurement for comparing the standard of living between two countries is the GDP in conjunction with the economic growth. GDP stands for Gross Domestic product.

The mean and standard deviation. If the data really are normally distributed, all other statistics are redundant.

a term that indicates a combined measurement of standard atmospheric pressure and room temperature. A+

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Linear Regression is a method to generate a "Line of Best fit" yes you can use it, but it depends on the data as to accuracy, standard deviation, etc. there are other types of regression like polynomial regression.

Best measurement for a phone book is cm or inches.