Range can include outliers that are not normal values and can skew overall data. Most relevant values can be found within one or two standard deviations on a normal curve.
standard deviation is best measure of dispersion because all the data distributions are nearer to the normal distribution.
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.
They are effectively the same but the standard deviation is more popular because the units of measurement are the same as those for the variable.
Are you talking of this in means of Statistics? If you are, then the variation from the mean is measured in standard deviation.
I will restate your question as "Why are the mean and standard deviation of a sample so frequently calculated?". The standard deviation is a measure of the dispersion of the data. It certainly is not the only measure, as the range of a dataset is also a measure of dispersion and is more easily calculated. Similarly, some prefer a plot of the quartiles of the data, again to show data dispersal.t Standard deviation and the mean are needed when we want to infer certain information about the population such as confidence limits from a sample. These statistics are also used in establishing the size of the sample we need to take to improve our estimates of the population. Finally, these statistics enable us to test hypothesis with a certain degree of certainty based on our data. All this stems from the concept that there is a theoretical sampling distribution for the statistics we calculate, such as a proportion, mean or standard deviation. In general, the mean or proportion has either a normal or t distribution. Finally, the measures of dispersion will only be valid, be it range, quantiles or standard deviation, require observations which are independent of each other. This is the basis of random sampling.
standard deviation is best measure of dispersion because all the data distributions are nearer to the normal distribution.
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.
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)
They are effectively the same but the standard deviation is more popular because the units of measurement are the same as those for the variable.
Are you talking of this in means of Statistics? If you are, then the variation from the mean is measured in standard deviation.
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 Absolute Measure of dispersion is basically the measure of variation from the mean such as standard deviation. On the other hand the relative measure of dispersion is basically the position of a certain variable with reference to or as compared with the other variables. Such as the percentiles or the z-score.
Standard deviation (SD) is a measure of the amount of variation or dispersion in a set of values. It quantifies how spread out the values in a data set are from the mean. A larger standard deviation indicates greater variability, while a smaller standard deviation indicates more consistency.
Units of measure do follow the standard deviation.
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.
Standard deviation is a measure of the spread of data.
The standard deviation is a measure of the spread of data.