Finding two unknowns from varience and mean

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The discussion revolves around determining the unknown values "a" and "b" from a discrete distribution with a specified mean of 6.5 and variance of 7.75. It is established that the sum of "a" and "b" equals 16, derived from the mean calculation. Participants express uncertainty about how to utilize the variance and standard deviation to find the specific values of "a" and "b." The standard deviation is calculated as the square root of the variance, but the method to apply this to the dataset remains unclear. Overall, the thread seeks a mathematical approach to solve for the unknowns using the provided statistical parameters.
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the data given below are from a discrete distribution with positive integer values.there are two values which are unknown, namely "a" and "b".

8,5,3,6,5,9,a,b

if the mean and varience respectively are 6.5 and 7.75, what are the possible values of "a" and "b"?


so far i have that a+b=16 since 3+5+5+6+8+9+a+b/8=6.5 and 6.5x8=64
3+5+5+6+8+9=36 and 64-36=16

i know that the square root of 7.75=2.783882...=standard deviation,but i don't know what to do with this information in order to find a and b
 
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How do you obtain variance from a set of data?
 
well you know that \sigma=\sqrt{var(x)} and you know var(x)...how do you find standard deviation from the set of data given?
 

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