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For the given data set, calculate the standard deviation (note this is a sample distribution, not a complete population distribution):

a) 97.9
b) 92.1
c) 112.3
d) 84.6

Answer :

Final answer:

The standard deviation of the given sample distribution is approximately 9.89.

Explanation

To calculate the standard deviation of a sample distribution, we first find the mean of the data points. Then, we calculate the squared differences between each data point and the mean. Next, we sum up these squared differences. After that, we divide the sum by the number of data points minus one (n-1), where n is the number of data points. Finally, we take the square root of this result to obtain the standard deviation.

Given data points: a) 97.9 b) 92.1 c) 112.3 d) 84.6

Step 1: Calculate the mean:

Mean = (97.9 + 92.1 + 112.3 + 84.6) / 4 = 386.9 / 4 = 96.725

Step 2: Calculate the squared differences from the mean:

(97.9 - 96.725)^2 = 1.42

(92.1 - 96.725)^2 = 21.62

(112.3 - 96.725)^2 = 243.22

(84.6 - 96.725)^2 = 147.23

Step 3: Sum up the squared differences:

Sum = 1.42 + 21.62 + 243.22 + 147.23 = 413.49

Step 4: Divide the sum by (n-1):

Standard deviation = √(413.49 / (4-1)) = √(413.49 / 3) ≈ √137.83 ≈ 11.74

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