Notes

Standard Deviation of AP Series

Standard Deviation for an Arithmetic Progression (AP) Series can be calculated using a simple formula given below: [{sigma ^2} = frac{{left( {n + 1} right)left( {n – 1} right)}}{{12}}{d^2}] [sigma = sqrt {frac{{left( {n + 1} right)left( {n – 1} right)}}{{12}}} cdot d] where (d) is the common difference in a AP series.

Different Formula for Variance & Standard Deviation

The formula for Variance: [{sigma ^2} = frac{{sumlimits_{i = 1}^n {{{left( {{X_i} – bar X} right)}^2}} }}{n}] It can also be written as follows: [{sigma ^2} = frac{{sum {left( {X_i^2 – 2bar X{X_i} + {{bar X}^2}} right)} }}{n}] [or,,,,{sigma ^2} = frac{{sum {X_i^2} – 2bar Xsum {{X_i}} + n{{bar X}^2}}}{n}] [or,,,,{sigma ^2} = frac{{sum {X_i^2} …

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Measures of Dispersion

Measures of Dispersion are the measure of the extent to which observations in a data set are close or far away from any given measure of central tendency. They are representative of homogeneity or heterogeneity of a distribution. The closer are the observations from their given central tendency, the more homogeneous is the distribution. The …

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