Final answer:
To find the standard deviation for the given data set, calculate the mean, find the deviations from the mean, square the deviations, calculate the mean of squared deviations, and take the square root.
Step-by-step explanation:
To find the standard deviation for the group of data items 15, 15, 15, 17, 19, 19, 19, you can use the following steps:
- Calculate the mean (average) of the data set. In this case, the mean is (15 + 15 + 15 + 17 + 19 + 19 + 19) / 7 = 17.
- Subtract the mean from each data item to get the deviations from the mean: (-2, -2, -2, 0, 2, 2, 2).
- Square each deviation to get the squared deviations: (4, 4, 4, 0, 4, 4, 4).
- Calculate the mean of the squared deviations: (4 + 4 + 4 + 0 + 4 + 4 + 4) / 7 = 4.
- Take the square root of the mean of the squared deviations to get the standard deviation: √4 = 2.
Therefore, the standard deviation for the group of data items is 2.