If I have 4 standard deviations, how do I find the SD of the distributions of all of them?

They are:
.15
.16
.14
.15

To find the standard deviation (SD) of a set of data, you can follow these steps:

1. Calculate the variance of the data set. Variance is the average of the squared differences from the mean.
- For each data point, subtract the mean of the data set from the data point.
- Square each result to get rid of negative values.
- Sum up all the squared differences.
- Divide the sum by the number of data points minus 1.

2. Take the square root of the variance to get the standard deviation.

Now, let's apply these steps to find the SD for the given set of data with standard deviations of 0.15, 0.16, 0.14, and 0.15.

Step 1: Calculate the variance
- For the first standard deviation of 0.15:
Variance = (0.15)^2 = 0.0225
- For the second standard deviation of 0.16:
Variance = (0.16)^2 = 0.0256
- For the third standard deviation of 0.14:
Variance = (0.14)^2 = 0.0196
- For the fourth standard deviation of 0.15:
Variance = (0.15)^2 = 0.0225

Step 2: Calculate the average variance
- Sum up all the variances: 0.0225 + 0.0256 + 0.0196 + 0.0225 = 0.0902
- Divide the sum by the number of data points (4 in this case): 0.0902 / 4 = 0.02255

Step 3: Calculate the standard deviation
- Take the square root of the average variance: √0.02255 ≈ 0.1502

Therefore, the standard deviation of the distribution of all the standard deviations is approximately 0.1502.