Question

There is a set of 100 observations with a mean of 46 and a standard deviation of 0. What is the value of the smallest observation in the set?

I think that the answer is 46.

Answer 1

what are the options

Answer 2

There are no options

Answer 3

well recall the standard deviation is just the square root of the mean squared deviation:$$\sigma=\sqrt{\frac1n\sum_{i=0}^n(x_i-\bar x)^2}$$if \(\sigma=0\) it follows that \(\sum\limits_{i=0}^n(x_i-\bar x)^2=0\)... since each term is positive the only way the sum can be \(0\) is if each deviation is \(0\) i.e. each observation is equal to our mean. in that case, you are correct that \(46\) is our smallest!

Answer 4

Thank you @oldrin.bataku for confirming my answer, I appreciate it

Answer 5

no problem!