Maintaining Mathematical Proficiency
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The standard deviation is the average amount by which each individual value deviates or differs from the mean.
About 7.09
We want to find the standard deviation of the given data set. The first thing that should be done is rearranging the numbers from least to greatest. 21, 26, 28, 29, 32, 44 Let's now proceed to finding the mean that we need to calculate the standard deviation.
Substitute values
The standard deviation of a set of data is the average amount by which each individual value deviates or differs from the mean. Standard Deviation sqrt((x_1-μ )^2+(x_2-μ )^2+... +(x_n-μ )^2/n) In the above formula, x_1, ... ,x_n are the values of the set of data, μ is the mean, and n is the number of values. For this exercise, the mean is 30 and there are 6 values in the data set. Let's use the value of the mean, 30, and apply the formula to each value in the set.
| x_n | x_n-μ | (x_n-μ)^2 |
|---|---|---|
| 30 | 30-21=9 | 9^2=81 |
| 30 | 30-26=4 | 4^2=16 |
| 30 | 30-28=2 | 2^2=4 |
| 30 | 30-29=1 | 1^2=2 |
| 30 | 30-32=-2 | (-2)^2=4 |
| 30 | 30-44=- 14 | (- 14)^2=196 |
| Sum of Values | ≈ 303 | |
Finally, we need to divide by 6 and then calculate the square root. Standard Deviation: sqrt(303/6)≈ 7.09 The standard deviation is about 7.09, so the typical value in the data set differs from the mean by about 7.09 units.