Question

If each observation of a data is increased by a constant 'K', then the arithmetic mean of new data:

• A. remains unchanged
• B. gets decreased by K
• C. gets increased by K
• D. gets multiplied by K

Hint:

Logic Tip: Addition or subtraction of a constant changes the mean by the same amount.

Answer 1

The Correct Option is C

Step 1:
If a constant value is added to every observation, the arithmetic mean also increases by the same constant.

Step 2:
Suppose original mean is: \[ \bar{X} \] If each observation is increased by $K$, new observations become: \[ X+K \]

Step 3:
The new arithmetic mean becomes: \[ \bar{X}+K \] Thus, the mean increases by $K$.

Step 4:
Therefore, the arithmetic mean: \[ \boxed{\text{gets increased by }K} \] Hence, the correct answer is: \[ \boxed{\text{(3) gets increased by K}} \]