Question 196975: 13, 10, 11, 8, 14, 13, 13, 14, 30
Within how many standard deviations of the mean do all of the above data values fall?
I think its 4 but I'm not sure.
Can someone explain to me how to do this?
Thank you!
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 13, 10, 11, 8, 14, 13, 13, 14, 30
Within how many standard deviations of the mean do all of the above data values fall?
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The mean is 14
The standard deviation is 6.325
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Ans: within 3 standard deviations.
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Cheers,
Stan H.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
First, calculate the mean. Find the sum of all your data points and divide by the number of data points.
Now, calculate the standard deviation.
Subtract each of your data points from the mean, then square the result. Once you have done that for each data point, add all of the squared differences. Divide that result by the number of data points minus 1, in this case you would divide by 8. Take the square root of that result giving you the standard deviation.
Add the standard deviation to the mean and subtract the standard deviation from the mean giving you a range. If all of your data points fall in that range, then your answer is 1.
If not, add 2 times the standard deviation to the mean and subtract 2 times the standard deviation from the mean giving you a new, larger range. Keep doing this, increasing the multiplier on the standard deviation by 1 each time until you create a range large enough to contain all of your data. Your answer will be equal to the last multiplier you used.
John
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