Download Sample SD vs Population SD

QMS 102
Population vs Sample - Variance and Standard Deviation
We only do calculations on samples to estimate corresponding
population parameters. ie
Therefore the formula for variance and standard deviation must be modified when used on a
sample data. As with the range, the sample calculation needs to be modified to get an
estim ate of the population Range.
QMS 102
Population vs Sample - Variance and Standard Deviation
Ex #1 Consider the population with one observation, 2. Clearly :=2 and the F = 0.
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2
Ex #2 Consider the sam ple with one observation, 3. 0'3 ˆ :.3
However there is no evidence about the population variance F.
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3
If the population m ean was known [a very unlikely situation] to be 2. Then an
estimate of the population variance would be (3-2)2/1=1.
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:
3
QMS 102
Population vs Sample - Variance and Standard Deviation
Ex #3 Consider the sam ple with two observations, 3 and 4.
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3
4
=(3+4)/2=3.5
However there is only one actual interval to indicate the population variance [even though
we divide this interval into two parts].
Effectively, the equivalent of one observation has been used to estimate
the mean, leaving the equivalent of n-1 "gaps" to estimate the
population variance. The number of left over observations is often
referred to as “degrees of freedom”
Sample Standard Deviation:
QMS 102
Population vs Sample - Variance and Standard Deviation
Use the calculator to compute
Sample Mean Firs t Four W eek= Firs t Four W eek =
Sample Variance First Four W eek = s 2 First Four W eek =
Sample Standard Deviation First Four W eek = s First Four W eek =
First Four W eeks: 5,6,12,15,18,4,5,4,14,21,0,7,8,9,16,6,6,12,22,25
Last W eek: 1,3,9,14,16
Sample Mean Last Week = Last Week =
Sample Variance Last Week = s 2 Last Week =
Sample Standard Deviation
Last Week
=s
Last Week
=
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