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1.2 Measures Of Measures Of Dispersion, Skwness And Kurtosis
The measures of dispersion is the defined as the how the set of observations dispersed or scattered. The measures of dispersion are:
- Quartile deviation or semi – interquartile range
- Mean deviation
- Standard deviation
The range is the difference between the largest observation and smallest observation.
Range = X Maximum – X Minimum
1.2.2 Quartile deviation or semi – interquartile range:
The quartile deviation is a measure describes about the 50 % of the data. The quartile deviation is denoted as Q.
Where Q3is the third quartile and Q1is the first quartile
1.2.3 Mean deviation:
Mean deviation explains about the deviation of the whole observation and it is a better measure than range and quartile deviation.
Mean deviation from the average is given as
Mean deviation =
Where fi is the frequency for the observation, Xi is the variables and N is the number of observations.
1.2.4 Standard deviation:
The standard deviation is the positive square root of the arithmetic mean of the squares of the deviations of the given values from their arithmetic mean. The population standard deviation is denoted as σ and the root mean square deviation as s.
Where (X bar) is the arithmetic mean, fi is the frequency for the observation, Xi is the variables and N is the number of observations.
The square of the standard deviation is called the variance
The root mean square deviation is
Where A is any arbitrary number, fi is the frequency for the observation, Xi is the variables and N is the number of observations.
The mean square deviation is
The standard deviation for the grouped or continuous frequency distribution is
Where f is the frequency for the observation, Xi is the variables, N is the number of observations, A is an arbitrary point and h is the common magnitude.
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