For the following set of data, find the sample standard deviation, to the nearest thousandth.
96, 63, 83, 78, 55, 96, 114, 52
To find the sample standard deviation, we first need to find the mean of the data set.
Mean = (96 + 63 + 83 + 78 + 55 + 96 + 114 + 52) / 8
Mean = 637 / 8
Mean = 79.625
Next, we calculate the squared differences from the mean for each data point, sum those squared differences, divide by n-1 (where n is the number of data points in the sample), and then take the square root of that sum to find the sample standard deviation.
Squared differences from the mean:
(96-79.625)^2 = 266.190
(63-79.625)^2 = 300.656
(83-79.625)^2 = 11.141
(78-79.625)^2 = 2.705
(55-79.625)^2 = 601.016
(96-79.625)^2 = 266.190
(114-79.625)^2 = 1215.681
(52-79.625)^2 = 760.423
Sum of squared differences = 3423.011
Sample standard deviation:
s = sqrt(3423.011 / (8-1))
s = sqrt(489.0027142857143)
s ≈ 22.122
Therefore, the sample standard deviation of the given data set is approximately 22.122.