I need help with this question

a) Suppose that a population only has one number, 50. What is its variance? b) Suppose that the mean of a sample with 10 observations is 11. Now a new observation is added to the sample. If the value of the new-added number is ll, will the mean of the new sample still be 11? Why or why not? c) Suppose that the mean and variance of a sample with 10 observations are 11 and 30, respectively. Now, a new observation is added to the sample. If the value of the 11th number is 11. What is the variance of the new sample? (1) Note that variance = (standard deviation) * (standard deviation) and that the standard deviation cannot be negative. For example, if the variance is 9, then the standard deviation is 3, not 3. Is it possible to have a sample with 10 integer numbers whose variance is smaller than its standard deviation? If yes, provide an example. If not, provide a short reason