Find the standard deviation for the given data. Round your answer to one or more decimal places than the original data.

3){15,13,31,42,58,78}

A)534.3 B)23.1 C)36.5 D)39.5

To find the standard deviation for the given data, follow these steps:

1. Calculate the mean (average) of the data set.
- Add all the numbers together: 15 + 13 + 31 + 42 + 58 + 78 = 237
- Divide the sum by the total number of values (6 in this case): 237 / 6 = 39.5

2. Calculate the difference between each data point and the mean.
- Subtract the mean from each data point:
15 - 39.5 = -24.5
13 - 39.5 = -26.5
31 - 39.5 = -8.5
42 - 39.5 = 2.5
58 - 39.5 = 18.5
78 - 39.5 = 38.5

3. Square each difference.
- Square each of the differences calculated in step 2:
(-24.5)^2 = 600.25
(-26.5)^2 = 702.25
(-8.5)^2 = 72.25
(2.5)^2 = 6.25
(18.5)^2 = 342.25
(38.5)^2 = 1482.25

4. Calculate the variance.
- Add up all the squared differences:
600.25 + 702.25 + 72.25 + 6.25 + 342.25 + 1482.25 = 3205.5
- Divide the sum by the total number of values (6 in this case): 3205.5 / 6 = 534.25

5. Take the square root of the variance to find the standard deviation.
- Calculate the square root: sqrt(534.25) ≈ 23.1

Therefore, the standard deviation for the given data is approximately 23.1.
The correct answer choice is B) 23.1