Which of the following is/are the Algebraic properties of the Arithmetic Mean ? i. The algebraic sum of…
The mean satisfies \(\sum(X_i-\bar X)=0\) and affine transformations act the same way on it, giving i and iii, (3). Squared deviations are minimised, not maximised, at the…
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Which of the following is/are the Algebraic properties of the Arithmetic Mean ?
i. The algebraic sum of deviation of different values from their arithmetic mean is zero.
ii. The sum of the squared deviations of the item from arithmetic mean is maximum.
iii. When each value is affected by a constant, the mean is also affected in the same way.
iv. From the arithmetic mean, it is possible to estimate the values given in the form of ratios and percentages.
Answer and explanation
Correct answer C
The mean satisfies and affine transformations act the same way on it, giving i and iii, (3). Squared deviations are minimised, not maximised, at the mean; division requires a nonzero divisor, and averaging percentages or ratios may need appropriate weights.
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