Statistical techniques

1) Write the formulae for the following concepts:
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Arithmetic Mean : Sum of observed values of a set divided by the number of observations in the set is called a mean or an average.
Median : In a set of observations, it is the value of the middlemost item when they are arranged in order of magnitude.
Mode : In a set of observations, it is the value which occurs with maximum frequency.
Coefficient of Variation : It is a relative measure of dispersion which is independent of the units of measurement. As opposed to this Standard Deviation is a pure number.
Range : It is the difference between the largest and the smallest observations of a given set of data.
Standard Deviation : It is the positive square root of the variance.
Variance : It is the arithmetic mean of squares of deviations of observations from their arithmetic mean.
Normal Equations : A set of simultaneous equations derived in the application of the least squares method, for example in regression analysis. They are used to estimate the parameters of the model.
Regression : It is a statistical measure of the average relationship between two or more variables in terms of the original units of the data.
Cyclical Variations : Oscillatory movements of a time series where the period  of oscillation, called cycle, is more than a year.
Irregular Movement : The random movement of time series, which is not explained by other components. In this sense it is a residual of other components.
Method of Least Squares : When a polynomial function is fitted to the time series, the method of least squares requires that the parameters of the function should be so chosen as to make the
sum of squares of the deviations between actual observations and expected values to be minimum.
Seasonal Variation : Periodical movement where the period is not longer than one year.
Secular Trend : The smooth, regular and long-term movement of a time series over a period of time. Trend may be upward or rising, downward or declining or it may remain more or less constant over time.
Source:IGNOU Study Material

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