The standard deviation of a set of data is a measure of how spread out the data is. To calculate the standard deviation, we first need to find the mean (average) of the data. The mean of the data 15, 16, 17, 18, and 19 is 16.8.

Next, we need to find the difference between each data point and the mean, and square each of these differences. This gives us the following:

(15 - 16.8)^2 = 1.44

(16 - 16.8)^2 = 0.64

(17 - 16.8)^2 = 0.04

(18 - 16.8)^2 = 1.44

(19 - 16.8)^2 = 2.24

Next, we need to add up all of these squared differences and divide by the number of data points (5 in this case). This gives us the variance of the data, which is 1.056.

Finally, to find the standard deviation, we simply take the square root of the variance. In this case, the standard deviation is 1.026. Therefore, the standard deviation of the data 15, 16, 17, 18, 19 is 1.026.