Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.
10)
{15, 13, 31, 42, 58, 78}
A)
36.5
B)
534.3
C)
39.5
D)
23.1
Well, it certainly isn't B; that is much too large. And it isn't C, because 39.5 is the mean. That leaves A) or D).
Are you familiar with the definition of standard deviation? You should go ahead and calculate it. It isn't that hard.
The individual deviations from the mean are: -24.5, -26.5, -8.5, 2.5, 18.5 and 38.5.
Next take the average of the SQUARES of those numbers: 534.3
The standard deviation is the square root of that number. (It is sometimes called the "root mean square")
To find the standard deviation for the given data, you can follow these steps:
1. Find the mean of the data set by adding up all the numbers and dividing by the total count. In this case, the mean is:
Mean = (15 + 13 + 31 + 42 + 58 + 78) / 6 = 237 / 6 = 39.5
2. Subtract the mean from each data point to get the deviation for each number. The deviations for the data set are:
(-24.5, -26.5, -8.5, 2.5, 18.5, 38.5)
3. Square each deviation to get the squared deviations. The squared deviations for the data set are:
(600.25, 702.25, 72.25, 6.25, 342.25, 1482.25)
4. Find the mean of the squared deviations by adding them up and dividing by the total count. In this case, the mean of the squared deviations is:
Mean of squared deviations = (600.25 + 702.25 + 72.25 + 6.25 + 342.25 + 1482.25) / 6 = 3205.5 / 6 = 534.25
5. Take the square root of the mean of the squared deviations to get the standard deviation. In this case, the standard deviation is:
Standard deviation = √534.25 ≈ 23.1
Therefore, the correct answer is D) 23.1.