Finding two unknowns from varience and mean

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The discussion focuses on determining the unknown values "a" and "b" from a discrete distribution with a specified mean of 6.5 and variance of 7.75. The equation derived from the mean calculation indicates that a + b equals 16. The standard deviation, calculated as the square root of the variance, is approximately 2.78. Participants seek methods to utilize the variance and standard deviation to solve for the unknowns effectively.

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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 [itex]\sigma=\sqrt{var(x)}[/itex] and you know var(x)...how do you find standard deviation from the set of data given?
 

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