Finding two unknowns from varience and mean

In summary, the data given represents a discrete distribution with positive integer values. The unknown values are "a" and "b". The mean and variance are given as 6.5 and 7.75, respectively. To find the possible values of "a" and "b", we can use the fact that a+b=16 and the formula for calculating standard deviation, \sigma=\sqrt{var(x)}. However, we still need to determine how to find the standard deviation from the given data.
  • #1
resresd
10
0
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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  • #2
How do you obtain variance from a set of data?
 
  • #3
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?
 

FAQ: Finding two unknowns from varience and mean

What is the formula for finding two unknowns from variance and mean?

The formula for finding two unknowns from variance and mean is:
x̄ = (a + b) / 2
s² = ((a - x̄)² + (b - x̄)²) / 2

How do you solve for the unknowns using the given variance and mean?

To solve for the unknowns, you can use the formula x̄ = (a + b) / 2 to find the average of the two unknown values. Then, plug this value into the formula s² = ((a - x̄)² + (b - x̄)²) / 2 and solve for either a or b. Once one of the unknowns is found, you can use this value to solve for the other unknown.

What is the significance of finding two unknowns from variance and mean?

Finding two unknowns from variance and mean can help in understanding the distribution of a set of data. It can also help in making predictions and drawing conclusions about the data set.

Can you find the unknowns if there is only one given value for variance and mean?

No, in order to find two unknowns from variance and mean, there must be two given values for each. If there is only one given value, there are an infinite number of possible solutions and the unknowns cannot be determined.

Are there any limitations to using variance and mean to find unknowns?

Yes, finding two unknowns from variance and mean assumes that the data follows a normal distribution. If the data is skewed or has outliers, this method may not accurately determine the unknown values.

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