Explanation:

Standard Deviation (SD) is a measure of the dispersion or variability of a set of data values. It is calculated as the square root of the variance.

When all the observations are multiplied by a constant, it affects the SD of the data. Let's see how:

- Effect of multiplying data by a constant: When all the observations in a data set are multiplied by a constant, it affects the measures of central tendency (mean, median, mode) and the measures of dispersion (range, interquartile range, variance, and SD) of the data. The effect on the measures of central tendency is straightforward - they are also multiplied by the same constant. The effect on the measures of dispersion is not as straightforward, and depends on the constant and the original SD of the data.

- New SD when all observations are multiplied by 2: When all the observations in a data set are multiplied by 2, the effect on the SD can be calculated as follows:

- The variance of the new data set is equal to the variance of the original data set multiplied by the square of the constant (2 in this case): Var(new) = Var(old) x 2^2 = 4Var(old)

- The SD of the new data set is equal to the square root of the variance of the new data set: SD(new) = √Var(new) = √(4Var(old)) = 2√Var(old)

- Therefore, the new SD is also multiplied by the constant (2 in this case).

- Example: Let's take an example to illustrate this. Suppose we have the following data set:

2, 4, 6, 8, 10

- The mean of this data set is 6.

- The SD of this data set is 2.83 (rounded to two decimal places).

- If we multiply all the observations by 2, we get:

4, 8, 12, 16, 20

- The mean of this new data set is 12.

- The SD of this new data set is 5.66 (rounded to two decimal places).

- The new SD is exactly twice the original SD, as predicted by our formula.

Therefore, the correct answer is option 'D': The new SD would be also multiplied by 2.