Stats Unit 1

Descriptive Statistics

Draws conclusions about a population by summarizing and organizing data. (The statement and data are collected from the SAME group)

Inferential Statistics

Draws conclusions and measures the reliability of conclusions based on information from a sample of the population. (The statement and data are collected from DIFFERENT groups)

What is a representative sample?

A sample that reflects the relevant characteristics of the population as closely as possible

Simple Random Sampling

Each item is equally likely to be the one obtained; Names in a box, table of random numbers, graphing calculator, or computer software

Sampling WITH vs WITHOUT Replacement

With: Can be selected MORE than ONCE

Without: Can ONLY be selected ONCE

Systematic Random Sampling

m=population size/sample size (truncated DOWN)

k,k+m,k+2m,k+3m . . .

Cluster Sampling

• Divide the population into clusters that are randomly selected, use ALL items in the chose clusters to form the sample
  

• 1. Divide pop into equally sized clusters, 2. Randomly generate numbers included in the number generated from the clusters

Stratified Sampling

Divide the population into SUBpopulations, by which a simple random sample is obtained that is proportional to the size of the subpopulation; combine samples from the subpopulation as the overall sample

Formula: 1. Add (A+B+C=X), 2. Divide (A/X, B/X, C/X), 3. Multiply: (A/X*100, B/X*100, C/X*100)

Multi-Stage Sampling

Combining sampling methods

Single-Value Grouping

ONE data value corresponding to each group, used when a FEW DISTINCT (DISCRETE) values are possible

Limit Grouping

SEVERAL values in each group, used only for DISCRETE data (90-99,80-89,70-79, . . ., 10-19, 0-9)

Cut-Point Grouping

SEVERAL values in each group, used only for CONTINUOUS data (90→100, 80→90, 70→80, . . ., 10→20, 0→10)
*from lower limit up to but NOT including the upper limit

Class Width

Calculated by subtracting the upper limit from the lower limit in Cut-Point Grouping

Mean

Average of values calculated by adding all the data values then dividing by the number of data values

Resistant vs Nonresistant Measures

• Mean, Range, and Standard Deviation ARE NOT resistant

• Median IS resistant

What denotes population mean?

Upper and Lowercase ‘mu’

X-Bar Formula

Sum of values over n (Sigma Xi/n)

What denotes sample mean?

X-Bar

A standardized variable has a mean ____ and standard deviation ____

0;1

Z-Score

X: Score
Mu: Mean
Sigma: Standard Deviation