Question

Arrange the following steps in sequence to find the variance of individual observations.
• [A.] Compute the mean \(\bar{X}\) of the given observations \(x_1, x_2, \ldots, x_n\).
• [B.] Square the deviations obtained and obtain the sum \(\sum_{i=1}^{n} (x_i - \bar{X})^2\).
• [C.] Divide the sum \(\sum_{i=1}^{n} (x_i - \bar{X})^2\) by \(n\).
• [D.] Take the deviations of the observations from mean i.e., \(x_i - \bar{X}, i=1,2,\ldots,n\).
Choose the correct answer from the options given below:

• A. A, B, C, D
• B. A, D, B, C
• C. A, C, B, D
• D. B, C, D, A

Hint:

Always follow: Mean → Deviations → Squaring → Averaging. This is the standard process for variance.

Answer 1

The Correct Option is B

Concept: Variance measures how far each observation deviates from the mean. The correct sequence follows logical statistical computation.

Step 1: Find the mean. We first compute: \[ \bar{X} = \frac{\sum x_i}{n} \] This corresponds to step A.

Step 2: Find deviations. Compute: \[ x_i - \bar{X} \] This corresponds to step D.

Step 3: Square deviations and sum. \[ \sum (x_i - \bar{X})^2 \] This corresponds to step B.

Step 4: Divide by total observations. \[ \sigma^2 = \frac{\sum (x_i - \bar{X})^2}{n} \] This corresponds to step C.

Step 5: Final order. \[ A \rightarrow D \rightarrow B \rightarrow C \] \[ \boxed{(2)} \]