It is expressed in terms of units in which the original figures are collected and stated. The Standard deviation is an absolute measure of dispersion. The square of the standard deviation is called variance As it is an absolute measure of variability, it cannot be used for the purpose of comparison. It gives more weight to extreme values because the values are squared up.ģ. It is not easy to understand and it is difficult to calculate.Ģ. It is the basis for measuring the coefficient of correlation and sampling.ġ. It is less affected by the fluctuations of sampling and hence stable.Ħ. It is possible for further algebraic treatment.ĥ. It is the most important and widely used measure of dispersion.Ĥ. As it is based on arithmetic mean, it has all the merits of arithmetic mean.ģ. It is rigidly defined and its value is always definite and based on all the observations and the actual signs of deviations are used.Ģ. Merits and Demerits of Standard Deviationġ. The formula for calculating standard deviation is as follows The standard deviation is denoted by s in case of sample and Greek letter s (sigma) in case of population. It is defined as the positive square-root of the arithmetic mean of the Square of the deviations of the given observation from their arithmetic mean. It is not suitable for mathematical treatment. It cannot be calculated from open-end class intervals.Ĥ. It is based on only two extreme observations.ģ. It is very much affected by the extreme items.Ģ. In certain types of problems like quality control, weather forecasts, share price analysis, etc.,ġ. S = Lower boundary of the lowest class = 60ģ. L = Upper boundary of the highest class = 75 Find the rangeĬalculate range from the following distribution. The yields (kg per plot) of a cotton variety from five plots are 8, 9, 8, 10 and 11. In continuous series, the following two methods are followed. In individual observations and discrete series, L and S are easily identified. This is the simplest possible measure of dispersion and is defined as the difference between the largest and smallest values of the variable. It should be simple to understand and easy to calculate It should lend itself for algebraic manipulation.ĥ. It should not be unduly affected by extreme items.Ĥ. There are different measures of dispersion like the range, the quartile deviation, the mean deviation and the standard deviation.Ĭharacteristics of a good measure of dispersionĪn ideal measure of dispersion is expected to possess the following propertiesģ. The scatterness or variation of observations from their average are called the dispersion. In addition to it we should have a measure of scatterness of observations. The first variety may be preferred since it is more consistent in yield performance.įorm the above example it is obvious that a measure of central tendency alone is not sufficient to describe a frequency distribution. There is greater uniformity of yields in the first variety whereas there is more variability in the yields of the second variety. It can be seen that the mean yield for both varieties is 42 kg but cannot say that the performances of the two varieties are same.
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