Final answer:
Adding or subtracting a constant to each sample value does not change the sample variance because the constant cancels out during the variance calculation process. Option C is correct.
Step-by-step explanation:
When a constant c is added to or subtracted from each value in a sample, the sample variance remains unchanged. This can be shown by going through the calculation of the variance step by step:
Calculate the sample mean before and after the addition or subtraction of the constant c.
Subtract each sample value from the mean, square the result, and then take the average of these squared differences to find the variance.
Note that adding or subtracting c affects both the sample values and the mean equally, so when we subtract the new mean from each of the new values, the constant c cancels out, leaving us with the same squared differences as before.
Therefore, the variance, which depends on these squared differences, does not change. The correct answer is c. The sample variance remains unchanged.