Discussion
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
Answer: B
The reasons are (i), (iii), (iv), (v).
The arithmetic mean is popular because it uses every observation (i), lends itself to further algebraic treatment, for instance combining group means (iii), is rigidly defined by a formula so everyone gets the same value (iv), and fluctuates less from sample to sample than most other averages (v).
Statement (ii) is false. The mean is most affected by extreme observations, because every value enters the sum; the median and mode are the averages that resist outliers. Every option containing (ii) is therefore wrong, and (i), (v) alone leaves out two genuine merits.
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