Q.Which of the following measures of dispersion is considered the most reliable, since it is based on every observation and permits further algebraic treatment?

The correct measure is the one that both uses every value in the data set and can be combined/manipulated algebraically for further statistical work.

Why (d) is correct: Standard Deviation is computed from the squared deviations of every observation from the mean, and because deviations are squared (not made absolute by ignoring sign, as in Mean Deviation), it obeys algebraic rules that allow variances of independent series to be combined — a property none of the other measures share. This is why S.D. is the preferred measure in advanced statistical work such as correlation, regression, and sampling theory.

Why the others are wrong:

1. Range uses only the two extreme values, ignoring every value in between.
2. Quartile Deviation ignores the smallest and largest 25% of the data.
3. Mean Deviation does use every observation, but taking absolute values (ignoring sign) makes it mathematically inconsistent for further algebraic treatment — this is the key distinction from Standard Deviation.
   ✓Final answer

   (d) Standard Deviation.

Choosing Mean Deviation because it also 'uses every observation,' while missing that its use of absolute values (not squares) is exactly what disqualifies it from further algebraic treatment.