The standard deviation for the set of numbers, 1,4,5,7,8 is nearly 2.45. If 10 are added to each number, then the new standard deviation will be

Options

A. 2.45 nearly
B. 24.45 nearly
C. 0.245 nearly
D. 12.45 nearly

Answer

To solve the problem, we need to understand how the standard deviation is affected when a constant is added to each number in a data set.

### Step-by-Step Solution:

1. **Identify the Original Data Set**:
The original numbers given are: 1, 4, 5, 7, 8.

2. **Understand the Standard Deviation**:
The standard deviation of the original set is given as approximately 2.45.

3. **Adding a Constant to Each Number**:
When we add a constant (in this case, 10) to each number in the data set, the new numbers will be:
- 1 + 10 = 11
- 4 + 10 = 14
- 5 + 10 = 15
- 7 + 10 = 17
- 8 + 10 = 18

So the new data set becomes: 11, 14, 15, 17, 18.

4. **Effect on Standard Deviation**:
The key property of standard deviation is that it measures the spread of the data points around the mean. When a constant is added to each data point, the mean increases by that constant, but the spread (or the distance of each data point from the mean) remains the same.

5. **Conclusion**:
Therefore, the new standard deviation will remain the same as the original standard deviation, which is approximately 2.45.

### Final Answer:
The new standard deviation will be approximately **2.45**.

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