Find the sample variance s2 for the following sample data. Round your answer to the nearest hundredth.
x:
23
17
12
35
29
To find the sample variance s^2, you can follow these steps:
1. Find the mean (x̄) of the sample data. To do this, add up all the values and divide the sum by the number of data points. In this case, the sum of the values is 23 + 17 + 12 + 35 + 29 = 116. Since there are 5 data points, the mean is 116/5 = 23.2.
2. Subtract the mean from each data point, and square the result. This will give you the squared deviations from the mean for each data point. In this case, the deviations are:
(23 - 23.2)^2 = 0.04
(17 - 23.2)^2 = 37.44
(12 - 23.2)^2 = 125.44
(35 - 23.2)^2 = 138.24
(29 - 23.2)^2 = 33.64
3. Find the sum of the squared deviations. Add up all the squared deviations from step 2. In this case, the sum is 0.04 + 37.44 + 125.44 + 138.24 + 33.64 = 334.8.
4. Divide the sum of the squared deviations by the number of data points minus 1 to find the sample variance. In this case, there are 5 data points, so you divide the sum of squared deviations by 5 - 1 = 4. Thus, the sample variance s^2 is 334.8 / 4 = 83.7.
Therefore, the sample variance s^2 for the given sample data is approximately 83.7.