Question 1202737: Consider the following test scores in a class of 34 students:
56, 60, 60, 61, 62, 63, 65, 66, 70, 70, 72, 73, 74, 74, 75, 75, 78, 78, 79, 80, 81, 85, 86, 87, 88, 88, 89, 89, 90, 94, 99, 99, 100, 100.
What is the standard deviation of these test scores? If necessary, round to at least 3 decimal places.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
I'm going to use a spreadsheet to do some of the scratch work.
The spreadsheet is linked here:
https://docs.google.com/spreadsheets/d/1Y08KiMCoCj8yuR3W4h7smamgP6Ot25NtMVF62HMMYTs/edit?usp=sharing
You do not need a google account to be able to access the spreadsheet.
That spreadsheet has a column of x values (column A)
Column B is subtracting mu = 78.41176 from each x value.
The value of mu is found by- Adding up the values, then
- Divide by the sample size n = 34
Column C is then squaring each item in column B
The label for column C is (x-mu)^2
The sum of column C is 5348.235294 approximately.
This is known as the Sum of Squared Error (SSE).
The population variance will have us divide the SSE by n = 34.
To get the sample variance, we divide SSE over n-1 = 34-1 = 33 instead.
population variance = SSE/n
population variance = 5348.235294/34
population variance = 157.301038058823
then
population standard deviation = sqrt(population variance)
population standard deviation = sqrt(157.301038058823)
population standard deviation = 12.5419710595593
population standard deviation = 12.542
Or
sample variance = SSE/(n-1)
sample variance = 5348.235294/(34-1)
sample variance = 5348.235294/33
sample variance = 162.067736181819
then
sample standard deviation = sqrt(sample variance)
sample standard deviation = sqrt(162.067736181819)
sample standard deviation = 12.7305827117937
sample standard deviation = 12.731
As for what you should pick for your final answer (population standard deviation vs sample standard deviation), I'm not sure.
The teacher's instructions appear to be vague.
In many realistic situations, the sample version is more preferred since we often won't know everything about the population.
However, your teacher might want to consider this group of 34 people as the entire population.
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