Final answer:
The standard deviation of the data set is 2.98, calculated by finding the mean, squaring the differences, averaging them, and taking the square root. One standard deviation below the mean is 2.52.
Step-by-step explanation:
To find the standard deviation of the data set 8.2, 10.1, 2.6, 4.8, 2.4, 5.6, 7.0, 3.3, follow these steps:
Calculate the mean (average) of the data set.
Subtract the mean from each data point and square the result.
Calculate the average of these squared differences.
Take the square root of the average to find the standard deviation.
Using a calculator or computer:
The mean of the data set is 5.5
The squared differences would be (8.2-5.5)^2, (10.1-5.5)^2, etc.
The average of these squared differences is approximately 8.86.
The square root of 8.86 gives us the standard deviation of approximately 2.98.
Therefore, the standard deviation of the data set, rounded to the nearest hundredth, is 2.98.
To find the value that is one standard deviation below the mean, you subtract the standard deviation from the mean:
5.5 - 2.98 = 2.52.