For the following set of data, find the sample standard deviation, to the nearest thousandth.
97, 163, 147, 246, 98, 38, 123
To find the sample standard deviation, we first need to calculate the mean of the data set:
(97 + 163 + 147 + 246 + 98 + 38 + 123) / 7 = 912 / 7 = 130.286
Next, we calculate the squared differences between each data point and the mean:
(97 - 130.286)^2 = 1171.306
(163 - 130.286)^2 = 1078.848
(147 - 130.286)^2 = 280.045
(246 - 130.286)^2 = 13215.965
(98 - 130.286)^2 = 1043.457
(38 - 130.286)^2 = 8497.118
(123 - 130.286)^2 = 53.643
Next, we calculate the sum of the squared differences:
1171.306 + 1078.848 + 280.045 + 13215.965 + 1043.457 + 8497.118 + 53.643 = 34640.382
Finally, we divide the sum of the squared differences by n-1 (sample size minus 1) and then take the square root of the result to find the sample standard deviation:
sqrt(34640.382 / 6) = sqrt(5773.397) ≈ 76.028
Therefore, the sample standard deviation of the data set is approximately 76.028 (rounded to the nearest thousandth).