Find the standard deviation for the given data. Round your answer to one
more decimal place than the original data.
2, 5, 47, 11, 13, 48, 39, 36
follow the steps on this page using your numbers.
http://www.gcseguide.co.uk/standard_deviation.htm
To find the standard deviation of a set of data, you can follow these steps:
Step 1: Find the mean (average) of the given data set.
Step 2: Subtract the mean from each data point to get the deviation from the mean.
Step 3: Square each deviation.
Step 4: Find the mean of the squared deviations.
Step 5: Take the square root of the mean of squared deviations to find the standard deviation.
Let's apply these steps to the given data set:
Step 1: Find the mean:
2 + 5 + 47 + 11 + 13 + 48 + 39 + 36 = 201
Mean = 201 / 8 = 25.125
Step 2: Find the deviation from the mean for each data point:
2 - 25.125 = -23.125
5 - 25.125 = -20.125
47 - 25.125 = 21.875
11 - 25.125 = -14.125
13 - 25.125 = -12.125
48 - 25.125 = 22.875
39 - 25.125 = 13.875
36 - 25.125 = 10.875
Step 3: Square each deviation:
(-23.125)^2 ≈ 535.64
(-20.125)^2 ≈ 405.06
(21.875)^2 ≈ 478.52
(-14.125)^2 ≈ 199.52
(-12.125)^2 ≈ 147.52
(22.875)^2 ≈ 522.52
(13.875)^2 ≈ 192.52
(10.875)^2 ≈ 118.52
Step 4: Find the mean of squared deviations:
(535.64 + 405.06 + 478.52 + 199.52 + 147.52 + 522.52 + 192.52 + 118.52) / 8 ≈ 328.265
Step 5: Take the square root of the mean of squared deviations:
√328.265 ≈ 18.115
Rounding to one more decimal place than the original data, the standard deviation of the given data set is approximately 18.1.