For the following set of data, find the sample standard deviation, to the nearest thousandth.
20, 41, 111, 111, 44, 52, 34, 52, 134
To find the sample standard deviation for the given data set, we first need to find the mean of the data set:
Mean = (20 + 41 + 111 + 111 + 44 + 52 + 34 + 52 + 134) / 9
Mean = 599 / 9
Mean = 66.556
Next, we calculate the squared differences between each data point and the mean:
(20 - 66.556)^2 = 2485.977
(41 - 66.556)^2 = 647.774
(111 - 66.556)^2 = 1573.528
(111 - 66.556)^2 = 1573.528
(44 - 66.556)^2 = 504.219
(52 - 66.556)^2 = 2114.697
(34 - 66.556)^2 = 1053.608
(52 - 66.556)^2 = 2114.697
(134 - 66.556)^2 = 4374.155
Next, we calculate the sum of these squared differences:
Sum = 2485.977 + 647.774 + 1573.528 + 1573.528 + 504.219 + 2114.697 + 1053.608 + 2114.697 + 4374.155
Sum = 15842.583
Now, we can calculate the sample variance:
Variance = Sum / (n - 1) = 15842.583 / 8 = 1980.322875
Finally, we find the square root of the sample variance to get the sample standard deviation:
Sample Standard Deviation = sqrt(1980.322875) = 44.514
Therefore, to the nearest thousandth, the sample standard deviation of the given data set is 44.514.