Question

A data set has arithmetic mean 25. If 10 is subtracted from each data print, what is the new arithmetic mean?

• A. 15
• B. 20
• C. 25
• D. 30

Answer 1

Answer:

A. 15

The Core Principle

If you add or subtract a constant value ($k$) from every single data point in a set, the mean of that set will also increase or decrease by that same constant.

Mathematically: $\text{New Mean} = \text{Old Mean} \pm k$

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Step-by-Step Solution

1. Identify the original mean: The initial mean is 25.

2. Identify the change: You are subtracting 10 from each data point.

3. Apply the rule:
   $\text{New Mean} = 25 - 10$

4. $\text{New Mean} = 15$

Conclusion

The new arithmetic mean is 15 (Option A)