Final answer:
The mean of the sample is 3, the degrees of freedom is 4, the variance is 2.75, and the standard deviation is approximately 1.66.
Step-by-step explanation:
To calculate the mean for the given sample, add up all the values and divide by the total number of values. Mean = (4 + 1 + 3 + 5 + 2) / 5 = 15 / 5 = 3.
The degrees of freedom for a sample is one less than the sample size, so in this case, the degrees of freedom would be 4.
To calculate the variance for the sample, find the squared difference between each value and the mean, sum up those squared differences, and divide by the number of values minus one. The squared differences are (4 - 3)^2, (1 - 3)^2, (3 - 3)^2, (5 - 3)^2, and (2 - 3)^2. The sum of these squared differences is 2 + 4 + 0 + 4 + 1 = 11. The variance is 11 / (5 - 1) = 2.75.
The standard deviation is the square root of the variance, so in this case, the standard deviation is √2.75 ≈ 1.66.