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

Options

A. 2.45
B. 24.5
C. 0.245
D. 12.45

Answer

To solve the problem, we need to determine the new standard deviation after adding 10 to each number in the original set. Let's break this down step by step.

### Step 1: Understand the effect of adding a constant to each number
When a constant is added to each number in a dataset, the mean of the dataset increases by that constant, but the standard deviation remains unchanged. This is because standard deviation measures the spread of the data points relative to the mean, and adding a constant shifts all data points equally without affecting their relative distances.

### Step 2: Identify the original standard deviation
The original standard deviation (SD) of the dataset {1, 4, 5, 7, 8} is given as 2.45.

### Step 3: Add 10 to each number
The new dataset after adding 10 to each number will be:
- Original numbers: {1, 4, 5, 7, 8}
- New numbers: {1+10, 4+10, 5+10, 7+10, 8+10} = {11, 14, 15, 17, 18}

### Step 4: Determine the new standard deviation
Since we established that adding a constant does not change the standard deviation, the new standard deviation remains the same as the original standard deviation.

### Conclusion
Thus, the new standard deviation after adding 10 to each number is still **2.45**.

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