Final answer:
The sample variance for the given sample is 27.78.
Step-by-step explanation:
To calculate the sample variance, we first need to calculate the mean of the sample. Given that the sum of the squares of the mean and its differences is 250, we can use this information to find the mean. Let's assume the mean is 'x'.
(x^2 + (10-x)^2) = 250
simplifying the equation: 2x^2 - 20x + 100 = 250
2x^2 - 20x - 150 = 0
Solving this quadratic equation, we get x = 6.5 or x = -5. We can ignore the negative value for the mean. Therefore, the mean (x) is 6.5.
Now, we can calculate the variance using the formula: variance = sum of (xi - x)^2 divided by n-1, where xi is each score in the sample and n is the sample size.
In this case, n = 10. Let's assume the scores are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Calculating the variance:
variance = [(1-6.5)^2 + (2-6.5)^2 + ... + (10-6.5)^2] / (10-1)
= [(5.5)^2 + (4.5)^2 + ... + (3.5)^2] / 9
= (30.25 + 20.25 + ... + 4.5) / 9
= 27.78