Final answer:
To calculate the standard deviation of the data set 19, 20, 20, 20, 20, 21, we find the mean, determine the squared deviations, calculate their mean (the variance), and then take the square root of this variance. The standard deviation is approximately 0.577.
Step-by-step explanation:
To find the standard deviation for the group of data items 19, 20, 20, 20, 20, 21, we follow these steps:
- Calculate the mean (average) of the data set.
- Subtract the mean from each data point and square the result (these are the squared deviations).
- Calculate the average of these squared deviations (this is the variance).
- Take the square root of the variance to get the standard deviation.
Here are the calculations:
The mean is (19 + 20 + 20 + 20 + 20 + 21) / 6 = 120 / 6
= 20.
The squared deviations are (19 - 20)^2, (20 - 20)^2, (20 - 20)^2, (20 - 20)^2, (20 - 20)^2, (21 - 20)^2.
These are 1, 0, 0, 0, 0, 1 respectively.
The variance is (1 + 0 + 0 + 0 + 0 + 1) / 6 = 2 / 6
= 0.333.
The standard deviation is the square root of 0.333, which is approximately 0.577.
Therefore, the standard deviation of the data set is approximately 0.577.