{9, 7, 13, 24, 32, 45, 47}
First you have to find the mean
The mean is
9+7+13+24+32+45+47=177/7=25.2857=25.29
Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.
{9, 7, 13, 24, 32, 45, 47}
(25.29-9)^2=16.29^2=265.36
(25.29-7)^2=18.29^2=334.52
(25.29-13)^2=12.29^2=151.04
(25.29-24)^2=1.29^2=1.66
(25.29-45)^2= -19.71^2=388.48
(25.29-47)^2= -21.41^2=458.39
1599.45
Sqrt 39.99
My answer isn't matching the possible choices
your mean is correct.
(25.29-9)^2=16.29^2=265.36
(25.29-7)^2=18.29^2=334.52
(25.29-13)^2=12.29^2=151.04
(25.29-24)^2=1.29^2=1.66
(25.29-45)^2= -19.71^2=388.48
(25.29-47)^2= -21.41^2=458.39
Your second moment about the mean is correct.
Now, standard deviation. I would divide that sum by n=7 (or in real life, n-1) then take the square root.
I get about 16
http://hubpages.com/hub/deviation
To calculate the standard deviation, you need to follow a specific formula. Here are the steps:
1. Find the mean of the given data. In this case, the mean is 25.29 (calculated correctly in your question).
2. For each data point, subtract the mean and square the result.
(9 - 25.29)^2 = 267.3841
(7 - 25.29)^2 = 338.5641
(13 - 25.29)^2 = 150.3241
(24 - 25.29)^2 = 1.6241
(32 - 25.29)^2 = 44.6441
(45 - 25.29)^2 = 392.2441
(47 - 25.29)^2 = 476.7841
3. Calculate the average of the squared differences. Add up all the squared differences and divide by the number of data points.
(267.3841 + 338.5641 + 150.3241 + 1.6241 + 44.6441 + 392.2441 + 476.7841) / 7 = 183.1679
4. Take the square root of the result obtained in step 3 to get the standard deviation.
√183.1679 ≈ 13.53 (rounded to two decimal places)
So, the correct standard deviation for the given dataset {9, 7, 13, 24, 32, 45, 47} is approximately 13.53. I apologize for any discrepancy in the calculation provided earlier.