Arithmetic mean is the most popularly used average because ............. . (i) It is based on all observations (ii) It is least affected by extreme observations (iii) It is capable of further mathematical treatments (iv) It is rigidly defined (v) It possesses sampling stability
(i), (iii), (iv), (v)
Judge each statement. (i) The arithmetic mean uses every observation in the data, so it is true.
(ii) The mean is the average most affected by extreme values (outliers), because every value enters the sum. This statement is false; the median and mode are the averages less affected by extremes.
(iii) The mean is capable of further algebraic treatment (for example, combined mean of groups, and the sum of deviations from the mean is zero), so it is true.
(iv) The mean has a rigid, precise formula, sum of observations divided by their number, so it is true. (v) Among averages, the mean varies least from sample to sample, so it has sampling stability and is true.
Hence, the answer is statements (i), (iii), (iv), (v).
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