Measures of Central Tendency

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A measure of central tendency is a single value that represents the center or typical value of a dataset. It is important because it: (1) Presents data in a concise form, (2) Shows special characteris…

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An ideal average should be: (1) Well defined and rigid, (2) Easy to understand and calculate, (3) Based on all observations, (4) Suitable for algebraic operations, (5) A stable measure across samples,…

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Arithmetic mean is the sum of all observations divided by the total number of observations. Formula: x̄ = Σx/n, where Σx is the sum of all observations and n is the number of observations.

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x̄ = A + (Σfd/n) × c, where A = assumed mean, d = (x-A)/c, f = frequency, c = class width, and n = total frequency (Σf).

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The sum of deviations of all observations from their mean is always zero. Symbolically: Σ(x - x̄) = 0. This is a unique property of arithmetic mean - deviations from any other value will not sum to ze…

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Combined mean formula: x̄c = (n₁x̄₁ + n₂x̄₂ + ... + nₖx̄ₖ)/(n₁ + n₂ + ... + nₖ). It is used when we know the means of two or more separate groups and want to find the mean of the combined group.

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Weighted mean is used when observations have different importance. Each observation is assigned a weight according to its importance. Formula: x̄w = Σwx/Σw, where w represents the weights assigned to …

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Geometric mean is the nth root of the product of n positive observations: G = ⁿ√(x₁ × x₂ × ... × xₙ). It should be used for calculating average rates of change, growth rates, or when dealing with rati…