Final answer:
To calculate the standard deviation of the given data set, first find the mean, then find the deviation of each value from the mean, square the deviations, find the mean of the squared deviations, and finally take the square root. The standard deviation is approximately 189.89.
Step-by-step explanation:
To calculate the standard deviation, follow these steps:
- Find the mean of the data set by adding all the numbers together and dividing by the total number of values. In this case, the mean is (1585 + 1690 + 1735 + 1890 + 1935 + 2021) / 6 = 1725.17.
- Subtract the mean from each individual value to find the deviation. The deviations for this data set are: (1585 - 1725.17), (1690 - 1725.17), (1735 - 1725.17), (1890 - 1725.17), (1935 - 1725.17), (2021 - 1725.17) = -140.17, -35.17, 9.83, 164.83, 209.83, 295.83.
- Square each deviation to eliminate negative values and calculate the squared deviations: 140.17^2, 35.17^2, 9.83^2, 164.83^2, 209.83^2, 295.83^2 = 19654.7089, 1236.8689, 96.4889, 27196.3489, 43911.0889, 87423.0889.
- Find the mean of the squared deviations by adding them together and dividing by the total number of values. In this case, the mean of the squared deviations is (19654.7089 + 1236.8689 + 96.4889 + 27196.3489 + 43911.0889 + 87423.0889) / 6 = 36004.1663.
- Take the square root of the mean of the squared deviations to find the standard deviation. In this case, the standard deviation is √36004.1663 ≈ 189.89.
Therefore, the standard deviation of the given data set is approximately 189.89.