Question 1084151: The
5
participants in a
200
-meter dash had the following finishing times (in seconds):
29, 24, 29, 29, 29
Assuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to at least two decimal places.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Answer: 2
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Explanation:
There are a few steps involved which will follow this basic outline
Step 1) Find the sample mean (xbar)
Step 2) Subtract the xbar value from each data point.
This list is the set of deviations from the mean.
Step 3) Square each result found in step 2.
This list is the set of squared deviations from the mean.
Step 4) Add up the results found in step 3.
This value is known as the sum of the squared deviations
Step 5) Divide the value found in the previous step by n = 5 to yield the population variance
Step 6) Apply the square root to the population variance to get the population standard deviation
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Let's follow the steps shown above
Step 1) Find the sample mean xbar
Add up the values. Divide the sum by 5 (since there are n = 5 values)
xbar = (Sum of the values)/5
xbar = (29+24+29+29+29)/5
xbar = 140/5
xbar = 28
The sample mean is xbar = 28
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Step 2) Subtract the sample mean from EVERY data value to form a new list
29-28 = 1
24-28 = -4
29-28 = 1
29-28 = 1
29-28 = 1
The differences are: 1, -4, 1, 1, 1
This new list {1, -4, 1, 1, 1} is the list of deviations from the mean.
In other words, it's the list of differences from the mean.
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Step 3) Square each result found in step 2 to get the list of squared deviations
(1)^2 = 1
(-4)^2 = 16
(1)^2 = 1
(1)^2 = 1
(1)^2 = 1
The results from above are: 1, 16, 1, 1, 1
The list of squared deviations from the mean is {1, 16, 1, 1, 1}
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Step 4) Add up each result found in the previous step to get the sum of the squared deviations.
This won't be a list. It'll be a single value.
1+16+1+1+1 = 20
The sum of the squared deviations is equal to 20
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Step 5) Divide the sum of the squared deviations (20) by n = 5 to get 20/5 = 4
The population variance is 4
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Step 6) Take the square root of population variance 4 to get sqrt(4) = 2
The population standard deviation is 2
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Other online resources to check out:
The first link is to a general article about standard deviation.
The second link is to an online calculator (free to use) to help check your answer.
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