![]() ![]() Another property this measure must have is to increase when the numbers get more different from each other and decrease when they get more similar. This measurement is commonly used to assess risk among stocks for risk-return. tn measures of dispersion (or spread) simplest measure of the dispersion of the data is the range tells how widely the data are dispersed range largest. From this we conclude that any measure of dispersion should be between 0 and (positive infinity). If it is known that all machines have a standard deviation of 2 pieces/hour, which one is worse assuming you want stability and predictability? The correct answer is the machine with the highest mean pieces/hour has less risk and is more predictable to generate consistent performance. In simple terms, it shows how squeezed or scattered the variable is. It is the extent to which the values vary around the central or average value. to know how much homogenous or heterogeneous the data is. The measure of dispersion is the measure of the spread of scores in a data set. Then you are interested in the mean and how much variability from the mean the machines exhibit. In statistics, the measures of dispersion help to interpret the variability of data i.e. In statistics, a measure of kurtosis is a measure of the tailedness of the probability distribution of a real-valued random variable. If we only know the standard deviation of the performance on 5 machines it may not be satisfactory to make a good decision if stability is most important. The standard deviation (commonly abbreviated to sd), is the usual measure of dispersion or variability that you will see in published papers. ![]() This formula is a definitional one and for calculations, an easier formula is used. SD is the square root of sum of squared deviation from the mean divided by the number of observations. It is a measure of spread of data about the mean. For example: Comparing variability is stocks, machines, operators, and shifts, commonly use the coefficient of variation. Standard deviation (SD) is the most commonly used measure of dispersion. ![]() This value is expressed as a percentage and helps to determine comparing variability when mean is also known. The coefficient of variation is the ratio of the standard deviation to the mean. ![]()
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