For the following set of data, find the sample standard deviation, to the nearest hundredth.
135, 187, 154, 108, 153, 176, 154, 174
135, 187, 154, 108, 153, 176, 154, 174
To find the sample standard deviation, you can follow these steps:
1. Calculate the mean of the data set:
Mean = (135 + 187 + 154 + 108 + 153 + 176 + 154 + 174) / 8
Mean = 1341 / 8
Mean = 167.63
2. Find the difference between each data point and the mean, square the result, and sum up all these squared differences:
(135 - 167.63)^2 = 1106.76
(187 - 167.63)^2 = 375.54
(154 - 167.63)^2 = 183.11
(108 - 167.63)^2 = 3546.42
(153 - 167.63)^2 = 215.92
(176 - 167.63)^2 = 70.56
(154 - 167.63)^2 = 183.11
(174 - 167.63)^2 = 39.94
Sum of squared differences = 6651.36
3. Divide the sum of squared differences by (n-1), where n is the number of data points in the sample (in this case, n = 8):
Variance = 6651.36 / (8-1)
Variance = 950.1943
4. Calculate the square root of the variance to get the sample standard deviation:
Sample standard deviation = √950.1943
Sample standard deviation ≈ 30.83
Therefore, the sample standard deviation of the given data set is approximately 30.83.