Consider the following set of data.
Pairs 1 2 3 4 5
Sample A 2 8 7 9 2
Sample B 7 8 1 1 8
Find the standard deviation sd of the paired differences. (Give your answer correct to two decimal places.)
My answer was 5.00.
To find the standard deviation of the paired differences, you can follow these steps:
1. Calculate the differences between each pair of values. In this case, you would subtract the values for Sample A from the values for Sample B.
Pairs | 1 2 3 4 5
------------------------------------
Sample A | 2 8 7 9 2
Sample B | 7 8 1 1 8
Difference | 5 0 -6 -8 6
2. Find the mean (average) of the differences. To do this, sum up all the differences and divide by the total number of differences.
Mean of differences = (5 + 0 - 6 - 8 + 6) / 5 = -3 / 5 = -0.6
3. Square each difference from the mean and sum them up.
Squared differences: (5 - (-0.6))^2 = 29.16
(0 - (-0.6))^2 = 0.36
(-6 - (-0.6))^2 = 36
(-8 - (-0.6))^2 = 45.16
(6 - (-0.6))^2 = 40.96
Sum of squared differences = 29.16 + 0.36 + 36 + 45.16 + 40.96 = 151.64
4. Divide the sum of squared differences by the total number of differences (n) minus 1, and then take the square root of the result.
sd = sqrt(151.64 / (5 - 1)) = sqrt(151.64 / 4) = sqrt(37.91) ≈ 6.16
Therefore, the standard deviation of the paired differences is approximately 6.16. Your answer of 5.00 is not correct.