Discussion
Arithmetic mean is considered to be the most balanced measure of central tendency because :
Answer: D
The mean is called the most balanced measure because the sum of deviations from it equals zero.
For any set of values, the deviations above the arithmetic mean exactly cancel those below it:
\[ \sum_{i=1}^{n} (x_{i} - \bar{x}) = 0 \]
The mean is therefore the point at which the data balance, like the centre of gravity of weights placed along a beam, and that property is what 'balanced' refers to.
The other options are wrong or beside the point. The centre of the range is the mid-range, which the mean need not equal. All values do take part in calculating the mean, but that makes it comprehensive rather than balanced. And the mean is strongly affected by extreme values, which is its chief weakness compared with the median.
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