Final Answer:
The standard deviation of the given data set {27, 27, 33, 21, 27} is approximately 4.110.
Step-by-step explanation:
To calculate the standard deviation, we follow these steps. First, find the mean of the data set. In this case, the mean is (27 + 27 + 33 + 21 + 27) / 5 = 27. Next, subtract the mean from each data point, square the result, sum up the squared differences, divide by the number of data points, and finally, take the square root of the result. The detailed calculations are as follows:
Mean = (27 + 27 + 33 + 21 + 27) / 5 = 27
Squared differences: (27-27)^2 + (27-27)^2 + (33-27)^2 + (21-27)^2 + (27-27)^2
= 0 + 0 + 36 + 36 + 0 = 72
Variance = 72 / 5 = 14.4
Standard Deviation = sqrt(14.4) ≈ 4.110
Therefore, the standard deviation of the given data set is approximately 4.110. The standard deviation provides a measure of the dispersion or spread of the data points around the mean. In this case, a higher standard deviation indicates a greater variability in the values of the data set.