Part of ALG-08 — Statistics: Mean, Variance & Standard Deviation

Arithmetic Mean — Three Computation Methods

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Three methods to compute mean for grouped data: (1) Direct: x-bar = sumfixiN\frac{fi*xi}{N}, best for small values. (2) Assumed Mean: x-bar = A + sumfidiN\frac{fi*di}{N} where di = xi - A, reduces computation. (3) Step Deviation: x-bar = A + h*sumfiuiN\frac{fi*ui}{N} where ui = xiAh\frac{xi-A}{h}, most efficient for equidistant classes. All three give identical results — choice depends on computational convenience. For JEE, direct method or step deviation is typically fastest.

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