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 first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
I'll let you do the calculations.
To find the sample variance, you need to follow these steps:
1. Calculate the sample mean (𝑥̅) of the sample data.
To do this, add up all the values in the sample and divide by the total number of values.
𝑥̅ = (23 + 17 + 12 + 35 + 29) / 5 = 116 / 5 = 23.2
2. Subtract the sample mean from each value in the sample and square the result.
(23 - 23.2)^2 = 0.04
(17 - 23.2)^2 = 38.44
(12 - 23.2)^2 = 125.44
(35 - 23.2)^2 = 138.24
(29 - 23.2)^2 = 33.64
3. Find the sum of all the squared differences calculated in step 2.
0.04 + 38.44 + 125.44 + 138.24 + 33.64 = 335.8
4. Divide the sum of squared differences by the total number of values minus 1 (n - 1).
𝑠^2 = 335.8 / (5 - 1) = 335.8 / 4 = 83.95
Therefore, the sample variance (𝑠^2) for the given sample data is approximately 83.95, rounded to the nearest hundredth.