Variance and standard deviation – UGC NET Question

Statement A correctly defines variance as the mean of squared deviations from the mean (in the population sense). Statement B is true because standard deviation is the positive square root of variance. Statement D is also correct since a larger standard deviation reflects more spread in the data. Statement C is false because if all observations are equal, both variance and standard deviation are zero. Statement E is false for the same reason. Therefore, A, B and D only are correct.

Option A:
Option A is incomplete; while A and B are true, it omits D and thus fails to connect standard deviation to dispersion.

Option B:
Option B is correct because it includes all three accurate statements and excludes C and E, both of which incorrectly deny the possibility of zero spread.

Option C:
Option C is wrong because it includes C (false), even though B and D are true.

Option D:
Option D is wrong because it includes E (false) and omits B (definition link), so it cannot be correct.