Question

The average of squared deviations from mean is called:

• A. Mean Deviation
• B. Variance
• C. Standard Deviation
• D. Coefficient of Variation

Hint:

Variance is measured in squared units. Standard deviation is the positive square root of variance: \[ \sigma=\sqrt{\sigma^2}. \]

Answer 1

The Correct Option is B

Concept: Variance is one of the most important measures of dispersion in statistics. For observations \[ x_1,x_2,\ldots,x_n \] with mean \(\bar{x}\), variance is defined as \[ \sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i-\bar{x})^2. \] Thus, variance is the average of the squared deviations from the arithmetic mean.

Step 1: Determine the quantity described in the question. A deviation from the mean is \[ x_i-\bar{x}. \] Its square is \[ (x_i-\bar{x})^2. \] Taking the average of all such squared deviations gives \[ \frac{1}{n} \sum_{i=1}^{n} (x_i-\bar{x})^2. \]

Step 2: Identify the statistical term. The above expression is exactly the definition of variance. Conclusion: \[ \boxed{\text{Variance}} \] Hence, the correct answer is Option (B).