When all the numbers on a list are the same, then the standard deviation of the list is zero. #Is it true or false?
2 Answers
True.
Explanation:
Standard deviation is a calculation that is based on summing all of the terms and their distance from the mean of all terms. If all the terms are the same value, then the value of the mean of all terms is just equal to the value of a term. This means when you take the distance of a term from the mean, it will be 0. Hence the sum of all these terms (regardless of the normalization factor) will be 0. So this statement is true.
Example (5 terms): 3, 3, 3, 3, 3
Mean = 3
So all terms - mean will be 3-3 = 0.
Sum of all 0s, is 0.
Hence standard deviation is 0.
True.
Explanation:
Think about this - the term "deviation" refers to how far a number is from a certain value (usually the mean). If every number is identical, there is no deviation. (The difference between every term and the average is 0.)
