Sample mean and sample variance

In summary, to find the two unknown values in a set of five data values with a sample mean of 104 and sample variance of 4, two equations can be used. The first equation is x + y = 213, where x and y are the two unknown values. The second equation is \sum_i x_i^2/n-(\bar x)^2 = 4, which is an alternative to the more complicated equation obtained from the sample variance.
  • #1
Shackman
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Homework Statement
The sample mean and sample variance of five data values are, respectively, 104 and 4. If three of the data values are 102 100 and 105, what are the other two values?The attempt at a solution
My idea was to get two equations for the two unknowns, let's call them x and y. The equation from the sample mean was easy enough to find.

(102 + 100 + 105 + x + y) / 5 = 104
102 + 100 + 105 + x + y = 520
x + y = 213

The equation obtained from the sample variance is way more difficult because of the algebra. I start off ((102-104)^2 + (100-104)^2 + (105 - 100)^2 + (x-104)^2 + (y-104)^2)/4 = 4. As you can see this will get messy in a hurry, when you substitute for x or y using the sample mean equation it will be a fourth degree polynomial. Is there an easier way to do this?
 
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  • #2
An alternative equation you can use is [itex]\sum_i x_i^2/n-(\bar x)^2[/itex] = 4.
 
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Related to Sample mean and sample variance

What is the sample mean?

The sample mean is a statistical measure that represents the average value of a set of data. It is calculated by adding all the values in the data set and dividing by the total number of values.

How is the sample mean different from the population mean?

The sample mean is calculated from a subset of the population, while the population mean represents the average of the entire population. The sample mean is often used as an estimate for the population mean.

What is the purpose of calculating the sample mean?

Calculating the sample mean allows us to summarize and understand the data set. It can also be used to make predictions about the population mean and to compare different data sets.

What is sample variance and why is it important?

Sample variance is a measure of how much the data values in a sample vary from the sample mean. It is important because it helps us understand the spread or dispersion of the data and can be used to make inferences about the population variance.

How is sample variance calculated?

Sample variance is calculated by finding the average of the squared differences between each data value and the sample mean. It is represented by the symbol 's2'. The formula for sample variance is: s2 = Σ(x - x̄)2 / (n - 1), where x is each data value, x̄ is the sample mean, and n is the sample size.

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