Find the sample standard deviation s for the following sample data. Round your answer to the nearest hundredth.
x: 23 20 11 33 27
Find the mean and the deviation of each score from the mean (x-mean). Square these deviations, then sum them and divide by n = number of scores. The square root of this value is your s.
To find the sample standard deviation (s), you need to follow these steps:
1. Find the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Find the sum of all squared differences.
4. Divide the sum of squared differences by n-1 (n represents the number of data points in the sample).
5. Take the square root of the result to get the sample standard deviation.
Let's calculate it for the given data set:
1. Find the mean:
Mean = (23 + 20 + 11 + 33 + 27) / 5 = 22.8
2. Subtract the mean from each data point and square the result:
(23 - 22.8)^2 = 0.04
(20 - 22.8)^2 = 8.24
(11 - 22.8)^2 = 138.24
(33 - 22.8)^2 = 122.44
(27 - 22.8)^2 = 17.64
3. Find the sum of all squared differences:
0.04 + 8.24 + 138.24 + 122.44 + 17.64 = 286.60
4. Divide the sum of squared differences by n-1:
286.60 / (5-1) = 71.65
5. Take the square root of the result to get the sample standard deviation:
√(71.65) ≈ 8.47
Therefore, the sample standard deviation (s) for the given sample data is approximately 8.47.