Question

Let the Arithmetic Mean of \(n\) observations be AM. If 5 is added to all the observations, then the new AM will be:

• A. AM + 5
• B. AM - 5
• C. AM
• D. AM + 5/n

Hint:

Exam Tip:
Effects of transformations on mean:

• Adding \(c\): Mean increases by \(c\).
• Subtracting \(c\): Mean decreases by \(c\).
• Multiplying by \(c\): Mean is multiplied by \(c\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The arithmetic mean is affected by changes in scale and location.
Adding a constant to all observations shifts the mean by that constant.

Step 2: Key Formula or Approach:
If each observation \(x_i\) is changed to \(x_i + c\), then the new mean is: \[ \text{New Mean} = \frac{\sum (x_i + c)}{n} = \frac{\sum x_i + nc}{n} = \frac{\sum x_i}{n} + c = \text{Old Mean} + c \]

Step 3: Detailed Explanation:
Here, \(c = 5\).
So, the new AM = AM + 5.

Step 4: Final Answer:
Therefore, option (A) is correct.