Question

The sum of the deviations of the observations 3, 4, 5, 6, 7 from their mean is:

• A. 0
• B. 5
• C. -5
• D. 6

Hint:

Exam Tip:
The sum of deviations from the mean is always 0.
This property is used to define variance and standard deviation.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The sum of deviations from the mean is always zero. This is a fundamental property of the arithmetic mean.

Step 2: Key Formula or Approach:
The mean of the observations is: \[ \bar{x} = \frac{3 + 4 + 5 + 6 + 7}{5} = \frac{25}{5} = 5 \] The deviations are: \[ 3 - 5 = -2, \quad 4 - 5 = -1, \quad 5 - 5 = 0, \quad 6 - 5 = 1, \quad 7 - 5 = 2 \] Sum of deviations: \[ -2 - 1 + 0 + 1 + 2 = 0 \]

Step 3: Final Answer:
Therefore, option (A) is correct.