The standard deviation of 25 observations is 4 and their mean is 25. If each observation is increased by 10, what is the new variance-

Options

A. (a) 4
B. (b) 14
C. c. 16
D. (d) 25.

Answer

To solve the problem step by step, we will follow these instructions:

1. **Identify the given data**:
- Number of observations (n) = 25
- Standard deviation (σ) = 4
- Mean (μ) = 25

2. **Calculate the variance of the original observations**:
- Variance (σ²) is the square of the standard deviation.
- So, Variance = σ² = 4² = 16.

3. **Understand the effect of increasing each observation**:
- When each observation is increased by a constant value (in this case, 10), the variance remains unchanged. This is because variance measures the spread of the data points relative to the mean, and adding a constant shifts the mean but does not affect the spread.

4. **Conclusion**:
- Therefore, the new variance after increasing each observation by 10 will still be 16.

### Final Answer:
The new variance is 16.

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