Question

Find the standard deviation of the set of data. {78,82,71,74,80}

Answer 1

The standard deviation of the set of data {78,82,71,74,80} is 4. The value that is one standard deviation below the mean is 73.

Step-by-step explanation:

To find the standard deviation of the set of data {78,82,71,74,80}, we follow these steps:

1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Calculate the average of those squared differences.
4. Take the square root of that average to get the standard deviation.

Let's do the calculations:

1. Mean = (78 + 82 + 71 + 74 + 80) / 5 = 385 / 5 = 77
2. Squared differences: (78 - 77)^2, (82 - 77)^2, (71 - 77)^2, (74 - 77)^2, (80 - 77)^2 which are 1, 25, 36, 9, and 9 respectively.
3. Average of squared differences = (1 + 25 + 36 + 9 + 9) / 5 = 80 / 5 = 16
4. Standard deviation = √16 = 4

Therefore, the standard deviation of the data set is 4. To find the value that is one standard deviation below the mean in our data set, we subtract one standard deviation from the mean: 77 - 4 = 73.