The population

Number = N

Mean =

Standard deviation =

The Population vs. The Sample

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)

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

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 population

Number = N

Mean =

Standard deviation =

Cannot afford to measure parameters of the whole population

So we draw a random sample.

The Population vs. The Sample

The sampleSample size = nSample mean = xSample standard deviation = s

Cannot afford to measure parameters of the whole population

So we draw a random sample.

The sampleSample size = nSample mean = xSample standard deviation = s

The population

Number = N

Mean =

Standard deviation =

The Population vs. The Sample

Does = x? Probably not. We need to be confident that x does a

good job of representing .

The sampleSample size = nSample mean = xSample 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

Random sampling error = (variation component) .or “standard error” (sample size component)

s = measure of variation

Use a square-root function of sample size

Standard error (OR random sampling error) = s .

(n-1)

Population mean = x + s .

(n-1)The population mean likely falls within some range around the sample mean—plus or minus a standard error or so.

(or “standard error”)

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?

Real-world Data & Visualization

• CIA World Factbook rankings

• https://www.cia.gov/library/publications/the-world-factbook/rankorder/rankorderguide.html

• Gapminder

• http://www.gapminder.org/world