Final Answer:
Range: 12
Sample Standard Deviation: 4.5826
Population Variance: 16.6667
Step-by-step explanation:
The range, a measure of dispersion, is calculated by subtracting the minimum value from the maximum. For this dataset {12, 15, 18, 21, 24}, the range is 12 (24 - 12 = 12). To find the sample standard deviation, first, determine the mean (sum of values divided by the count).
The mean is 18 (12 + 15 + 18 + 21 + 24 = 90, 90 ÷ 5 = 18). Then, calculate the differences between each value and the mean, square those differences, sum them up, divide by (n - 1), and take the square root to get the sample standard deviation, which is approximately 4.5826.
The population variance, a measure of how spread out the values in a population are, is the square of the standard deviation. For this dataset, the population variance is approximately 16.6667 (4.5826 squared).
Here is complete question;
"Determine the range, the sample standard deviation, and the population variance of the following data?
Data set: {12, 15, 18, 21, 24}"