Explanation:
To understand why the new standard deviation will be the same as the original standard deviation, we need to understand the concept of standard deviation and how it is affected by adding a constant to each data point.

Standard Deviation:
The standard deviation measures the spread or dispersion of a set of data points. It tells us how much the data points deviate from the mean. A higher standard deviation indicates a greater spread of data points, while a lower standard deviation indicates a smaller spread.

Effects of Adding a Constant to Data Points:
When a constant is added to each data point, it does not affect the spread or dispersion of the data points. It simply shifts the entire distribution by the same amount. This means that the new data points will have the same relative distances from each other as the original data points.

Effect on Standard Deviation:
Since the standard deviation measures the spread or dispersion of the data points, adding a constant to each data point does not change the spread. The new standard deviation will be the same as the original standard deviation.

Proof:
Let's assume the original standard deviation is S. Adding the constant C to each data point will result in new data points: a+C, b+C, and c+C.

To calculate the new standard deviation, we need to calculate the variance of the new data points:

Variance = ((a+C - (a+b+c+C)/3)^2 + (b+C - (a+b+c+C)/3)^2 + (c+C - (a+b+c+C)/3)^2) / 3

Expanding and simplifying the above expression, we get:

Variance = ((a - (a+b+c)/3)^2 + (b - (a+b+c)/3)^2 + (c - (a+b+c)/3)^2) / 3

This is the same as the original variance, which is equal to S^2.

Therefore, the new standard deviation is equal to the original standard deviation S.

Hence, the correct answer is option 'A'. The new standard deviation will be S.