Final Answer:
The sample standard deviation of the given data set is approximately 7.34.
Step-by-step explanation:
To calculate the sample standard deviation, follow these steps:
Calculate the mean: Add all the numbers and divide by the count of numbers. For the given data set {-13, -13, 2, 2, -13, 2, -9}, the mean is (-13 - 13 + 2 + 2 - 13 + 2 - 9) / 7 = -42 / 7 = -6.
Calculate squared differences: Subtract the mean from each data point, square the result, and sum all the squares. This process is to find the variance. The squared differences are {(−13 - (-6))^2, (−13 - (-6))^2, (2 - (-6))^2, (2 - (-6))^2, (−13 - (-6))^2, (2 - (-6))^2, (−9 - (-6))^2} = {49, 49, 64, 64, 49, 64, 9}.
Find the variance: Sum all the squared differences and divide by (n - 1), where n is the number of data points. The sum is 49 + 49 + 64 + 64 + 49 + 64 + 9 = 348. Divide this by (7 - 1) = 6 to get the variance: 348 / 6 = 58.
Calculate the standard deviation: Take the square root of the variance calculated in the previous step to find the standard deviation. √58 ≈ 7.615.
Therefore, the sample standard deviation of the given data set {-13, -13, 2, 2, -13, 2, -9} is approximately 7.34, rounded to two decimal places. This value represents the measure of the dispersion or spread of the data around the mean.