For the following set of data, find the population standard deviation, to the nearest thousandth.
71, 27, 57, 15, 92, 66, 85
To find the population standard deviation, you can follow these steps:
1. Find the mean of the data:
(71 + 27 + 57 + 15 + 92 + 66 + 85) / 7 = 313 / 7 = 44.714 (rounded to three decimal places)
2. Find the squared difference between each data point and the mean:
(71 - 44.714)^2 = 754.162
(27 - 44.714)^2 = 310.500
(57 - 44.714)^2 = 151.156
(15 - 44.714)^2 = 862.331
(92 - 44.714)^2 = 2225.677
(66 - 44.714)^2 = 485.885
(85 - 44.714)^2 = 1610.920
3. Find the sum of those squared differences:
754.162 + 310.500 + 151.156 + 862.331 + 2225.677 + 485.885 + 1610.920 = 5300.631
4. Divide the sum by the total number of data points (7) to calculate the population variance:
5300.631 / 7 = 757.233
5. Take the square root of the variance to find the population standard deviation:
√757.233 ≈ 27.52 (rounded to three decimal places)
Therefore, the population standard deviation for the given data set is approximately 27.520.