For the following set of data, find the sample standard deviation, to the nearest thousandth.
27, 19, 20, 20, 20, 21, 18, 21, 20
27, 19, 20, 20, 20, 21, 18, 21, 20
Original data: 27, 19, 20, 20, 20, 21, 18, 21, 20
1. Find the mean:
mean = (27 + 19 + 20 + 20 + 20 + 21 + 18 + 21 + 20) / 9
mean = 186 / 9
mean = 20.67
2. Find the differences between each data point and the mean:
7.33, -1.67, -0.67, -0.67, -0.67, 0.33, -2.67, 0.33, -0.67
3. Square each difference:
53.7889, 2.7889, 0.4489, 0.4489, 0.4489, 0.1089, 7.1289, 0.1089, 0.4489
4. Find the sum of the squared differences:
65.3013
5. Calculate the variance:
variance = sum of squared differences / (n - 1)
variance = 65.3013 / 8
variance = 8.1626625
6. Calculate the sample standard deviation:
sample standard deviation = square root of variance
sample standard deviation = √8.1626625
sample standard deviation ≈ 2.858
Therefore, the sample standard deviation for the given data set is approximately 2.858.