UGC NET Questions (Paper – 1)

This option is correct because standard deviation measures the spread of data around the mean and is defined using squared deviations. Squaring removes negative signs before averaging and taking the square root. The square root of a non-negative number is also non-negative. Therefore, standard deviation cannot be negative and is always non negative.

Option A:
Standard deviation can be zero only in the special case where all observations are equal to the mean. In most real data sets, values vary, giving a positive spread. Hence, "always zero" is incorrect.

Option B:
Although different data sets can have different standard deviations, the value is never negative. It can be zero or positive depending on the variation in the data. This means the correct description is that standard deviation is always non negative.

Option C:
"Always one" would suggest that every data set has the same fixed amount of spread, which is not true. Different data sets can have very large or very small variability. Therefore, this option is wrong.

Option D:
Saying standard deviation may be negative contradicts the mathematical definition involving squared deviations and square roots. Since squares are non negative, their average and square root cannot be negative either. Thus, this option is mathematically impossible.

Variance is defined as the square of the standard deviation. Since standard deviation is the square root of variance, squaring the standard deviation gives the variance (a measure of dispersion).

Option A:
Variance is correct because it equals (standard deviation)² and measures how spread out data are around the mean using squared deviations.

Option B:
Mean is a measure of central tendency (average), not the square of standard deviation, so it does not match the definition.

Option C:
Range is max − min, another dispersion measure, but it is not equal to (standard deviation)².

Option D:
Median is the middle value of ordered data and is unrelated to squaring the standard deviation.