Standard deviation spread measure – UGC NET Question

Standard deviation is defined as the positive square root of the variance and summarises how far, on average, scores deviate from the mean. A larger standard deviation indicates greater dispersion, while a smaller one suggests that scores cluster closely around the mean. It is widely used in both descriptive and inferential statistics to quantify variability and to compute standard errors. Therefore, the spread measure described in the stem is known as the standard deviation.

Option A:
The standard deviation provides a measure in the same units as the original scores, making it easier to interpret than the variance. It plays a central role in normal distribution theory and confidence interval estimation. These properties align precisely with what the question is describing.

Option B:
The mean is the arithmetic average (a measure of central tendency), not a measure of dispersion computed as the square root of variance. It tells where the centre of the distribution lies, but it does not quantify spread around the mean. Therefore, mean does not fit the stem.

Option C:
Quartiles divide an ordered dataset into four parts, and measures based on quartiles (like interquartile range) describe spread differently. “Quartile” itself is not defined as the square root of variance, so it cannot complete the term “_____ deviation” correctly here.

Option D:
The coefficient of variation is the standard deviation divided by the mean (often expressed as a percentage) and is used to compare relative variability across different scales. It is derived from standard deviation rather than being the square root of variance itself. Hence, it is not the correct completion.