Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13.
Answer Details
To calculate the standard deviation, we need to first find the mean (average) of the data.
Mean = (7 + 8 + 9 + 10 + 11 + 12 + 13) / 7 = 10
Next, we need to find the difference between each data point and the mean, and square the differences.
(7-10)^2 = 9
(8-10)^2 = 4
(9-10)^2 = 1
(10-10)^2 = 0
(11-10)^2 = 1
(12-10)^2 = 4
(13-10)^2 = 9
Then, we add up all of these squared differences and divide by the total number of data points.
(9 + 4 + 1 + 0 + 1 + 4 + 9) / 7 = 28 / 7 = 4
Finally, we take the square root of this result to find the standard deviation.
Standard deviation = √4 = 2
Therefore, the standard deviation of the given data is 2.