Statistics

Population

Entire group of individuals from whom information is gathered

Sample

Subset of individuals in the population from which the data is collected

Convenience sample

Sampling individuals who are easy to reach

Voluntary response

People who choose to be in a sample

Simple Randoms Sampling (SRS)

Every group is equally likely to be chosen

How do you conduct SRS?

Label, randomize, and select

µ

Population mean

σ

Standard deviation

x̄

Sample mean

Which sampling methods are biased? Why?

Voluntary response and convenience sampling because they don’t represent the entire population

Individual

What’s being surveyed/where the data is being collected

Variable

Thing being studied/what changes

Are people individuals or variables?

Individuals

Is hair color a variable or individual?

Variable

Categorial/Qualitative data

Variable that assigns labels that place each individual into a particular group; data representing information and concepts that are not represented by numbers (ex: hair color, roll of a die)

Quantitative variable

Takes number values that are quantities, counts, or measurements (ex: number of dog breeds)

Distribution

Tells what values a variable takes and how often it takes those values

Median

The midpoint of distribution such that about half of the observations are smaller and about half of them are greater

Ordered set

Data set from smallest to largest

Odd numbered sets are…

Exactly half

Standard Deviation

Measures the typical distance of the values in a distribution from the mean

The smaller the σ…

The less variability

Quartiles

Divide ordered sets into four groups having roughly the same number of values

Q1

Median distance of data values to left of median

Q3

Median distance of data values to right of median

Density curve

Always on or above horizontal axis and has area of exactly 1 underneath it; an estimate proportion of the data set

Median of density curve

Equal-areas point/the point that divides the curve in half

Mean of density curve

Point at which curve would balance if made of solid material; at the center of mass

Normal distribution

A symmetric, single-peaked, bell-shaped density curve called a Normal curve

Normal distribution is specified by…

µ (mean) and σ (standard deviation)

Empirical Rule/68-95-99.7 Rule

Only applies to Normal distribution; in a Normal distribution with µ and σ, approximately 68% of data falls within a distance of 1σ, approx. 95% of data falls within a distance of 2σ, and approx. 99.7% of data falls within a distance of 3σ of the µ