High School

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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