Statistical Concepts: Sampling and Probability

Parameter vs. Statistic

Parameter: Population (μ, σ)

Statistic: Sample (x̄, s)

Rules of Probability

1. 0 ≤ P(x) ≤ 1
2. Σ P(x) = 1
3. P(not x) = 1 - P(x)

Central Limit Theorem

As n (sample size) gets bigger, the sample distance will become approximately normal (shape).

Law of Large Numbers

As n gets bigger, the sample mean (x̄) will get closer to the population mean (μ) (number).

68-95-99.7 Rule

• 68% of data will lie within 1 standard deviation of the mean (σ + μ)
• 95% of data will lie within 2 standard deviations of the mean (2σ + μ)
• 99.7% of data will lie within 3 standard deviations of the mean (3σ + μ)

Sampling Types

Simple Random Sampling (SRS): Normal, random picking.

Systematic Sampling: Every kth sample.

Stratified Sampling: Groups are put together based on similarity, then some samples are taken from groups.

Cluster Sampling: Groups are put together based on similarity, then all of the group is taken as a sample.

Five-Number Summary

Parent Norm vs. Parent Skew

One sample:

For "Distribution of Sample": x̄ = μ

Multiple samples: s = σ / √n

Proportion/Probability

• Find z-score.
• Put into the applet.
• Shade the correct sides based on "less than" or "more than".

Percentile

• Shade to the LEFT, put the percentile in the top.
• Get the z-score from the bottom.
• Solve for x: x = zσ + μ

LESS: Z-

MORE:

Z+

Extreme or More Extreme: