#### The Population vs. The Sample

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The Population vs. The Sample

The Population vs. The Sample
The population
Number = N
Mean = m
Standard deviation = s
Cannot afford to measure
parameters of the whole population
We will likely never know these
(population parameters - these
are things that we want to know
about in the population)
3 Types of Samples
• Haphazard sampling
– Convenience or self-selection
• Quota sampling
– Categories and proportions in the population
• Probability sampling
– Random sampling
– Multistage cluster sampling
– accuracy (margin of error) & confidence level
The Population vs. The Sample
The population
Number = N
Mean = m
Standard deviation = s
Cannot afford to measure
parameters of the whole population
So we draw a random sample.
We will likely never know these
(population parameters - these
are things that we want to know
about in the population)
The Population vs. The Sample
The sample
Sample size = n
Sample mean = x
Sample standard
deviation = s
Cannot afford to measure
parameters of the whole population
So we draw a random sample.
The Population vs. The Sample
Does m = x? Probably not. We
need to be confident that x does a
good job of representing m.
The population
Number = N
Mean = m
Standard deviation = s
The sample
Sample size = n
Sample mean = x
Sample standard
deviation = s
Connecting the Population Mean to the Sample Mean
How closely does our sample mean resemble the population mean
(a “population parameter” in which we are ultimately interested)?
Population parameter = sample statistic + random sampling error
(or “standard error”)
Random sampling error = (variation component) .
or “standard error”
(sample size component)
Use a square-root
function of sample size
Standard error (OR random sampling error) =
Population mean =
x+
s .
(n-1)
The sample
Sample size = n
Sample mean = x
Sample standard
deviation = s
s .
(n-1)
The population mean likely falls within
some range around the sample mean—
plus or minus a standard error or so.
To Compute Standard Deviation
• Population standard deviation
• Sample standard deviation
Why Use Squared Deviations?
• Why not just use differences?
– Student A’s exam scores/(Stock A’s prices):
– 94, 86, 94, 86
• Why not just use absolute values?
– Student B’s exam scores/(Stock B’s prices):
– 97, 84, 91, 88
– Which one is more spread out /unstable /risky
/volatile?
is the formula for:
A.Population standard deviation
B.Sample standard deviation
C.Standard error
D.Random sampling error
E.Population mean