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For the following set of data, find the sample standard deviation, to the nearest thousandth.

162, 75, 49, 160, 63, 116, 57

162, 75, 49, 160, 63, 116, 57

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:

https://brainly.com/question/16555520

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