Find the sample variance s2 for the following sample data. Round your answer to the nearest hundredth.
x: 23 17 12 35 29
Find the mean and the deviation of each score from the mean. Square these deviations and add them. Divide that sum by n (5) to get the variance.
To find the sample variance, s^2, you can follow these steps:
1. Calculate the mean (average) of the sample data. Add all the values and divide by the total number of values.
Mean = (23 + 17 + 12 + 35 + 29) / 5 = 116 / 5 = 23.2
2. Subtract the mean from each of the data points and square the result. This step is called finding the deviation.
Deviation = (23 - 23.2)^2 + (17 - 23.2)^2 + (12 - 23.2)^2 + (35 - 23.2)^2 + (29 - 23.2)^2
3. Calculate the sum of all the squared deviations.
Sum of squared deviations = (0.04) + (36.04) + (133.44) + (138.24) + (33.64) = 341.4
4. Divide the sum of squared deviations by (n - 1), where n is the sample size. In this case, n is 5.
s^2 = 341.4 / (5 - 1) = 341.4 / 4 = 85.35
5. Round your answer to the nearest hundredth.
s^2 ≈ 85.35 (rounded to the nearest hundredth)
Therefore, the sample variance, s^2, for the given sample data is approximately 85.35.