Final answer:
To calculate the standard deviation, you need to follow a few steps. In this case, the standard deviation of the given data set is approximately 227.4.
Step-by-step explanation:
To calculate the standard deviation of a data set, you can follow these steps:
- Find the mean (average) of the data set.
- Subtract the mean from each data point and square the result.
- Find the mean of the squared differences.
- Take the square root of the mean from step 3 to get the standard deviation.
For the given data set: 3, 4, 5, 6, 2, 3, 12, 79, 5, 694.2, 26.3, 24.8, 616.9, the mean is 122.89. Next, subtract the mean from each data point:
-119.89, -118.89, -117.89, -116.89, -120.89, -119.89, -110.89, -43.89, -117.89, 571.31, -96.59, -98.09, 494.01.
Square each of these differences:
14307.12, 14138.32, 13978.92, 13830.32, 14607.12, 14307.12, 12289.12, 1928.12, 13868.92, 326447.03, 9316.46, 9617.68, 244117.84.
Find the mean of these squared differences:
51679.30154.
Finally, take the square root of the mean to find the standard deviation:
Standard deviation = √51679.30154 = 227.37 (rounded to the nearest tenth).