Answer :
The sample standard deviation of the given data set is approximately 49.162.
To calculate the sample standard deviation, we first need to calculate the sample mean:
Mean = (162 + 75 + 49 + 160 + 63 + 116 + 57) / 7
= 682 / 7
= 97.43
Next, the deviation of each data point from the mean:
162 - 97.43 = 64.57
75 - 97.43 = -22.43
49 - 97.43 = -48.43
160 - 97.43 = 62.57
63 - 97.43 = -34.43
116 - 97.43 = 18.57
57 - 97.43 = -40.43
Then, we square each deviation:
64.57² = 4168.88
(-22.43)² = 502.20
(-48.43)² = 2342.16
62.57² = 3921.02
(-34.43)² = 1184.84
18.57² = 344.89
(-40.43)² = 1634.99
Next, we add up all the squared deviations:
4168.88 + 502.20 + 2342.16 + 3921.02 + 1184.84 + 344.89 + 1634.99 = 14499.98
We then divide the sum of the squared deviations by n-1 (where n is the number of data points) to get the sample variance:
Sample variance = 14499.98 / (7 - 1) = 2416.6633
Finally, we take the square root of the sample variance to get the sample standard deviation:
Sample standard deviation = √2416.6633 = 49.162 (rounded to the nearest thousandth)
Therefore, the sample standard deviation of the given data set is approximately 49.162.
Learn more about the standard deviation here:
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