1. The Population vs. The Sample
We will likely never know these (population parameters—these are things that we want to know about in the population)
The population
Number = N
Mean = m
Standard deviation = s
Cannot afford to measure parameters of the whole population

2. Types of Samples Haphazard sampling Quota 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

3. The Population vs. The Sample
We will likely never know these (population parameters—these are things that we want to know about in the population)
The population
Number = N
Mean = m
Standard deviation = s
Cannot afford to measure parameters of the whole population
So we draw a random sample.

4. 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.

5. 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

6. 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
The sample Sample size = n Sample mean = x Sample standard deviation = s
s = measure of variation
Standard error (OR random sampling error) = s Ö (n-1)
Population mean = x s Ö (n-1)
The population mean likely falls within some range around the sample mean—plus or minus a standard error or so.

7. To Compute Standard Deviation
Population standard deviation
Sample standard deviation

8. 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?

10. Real-world Data & Visualization
CIA World Factbook rankings
Gapminder