Stats 240 Unit 1

Statistics

Branch of mathematics that deals with the organization, analysis, and interpretation of data

Data

Number you get from counting or measuring

Branches of statistics

Descriptive and inferential

Descriptive

Describe data from our sample

Inferential

We use data from our sample to draw inferences about the larger population from which the sample was drawn

Individuals

The things that make up our samples

Variables

Properties of individuals we are interested in

Population

group of things that we draw conclusions about

Sample

Subset of population

Samples of convenience

Members of the population to which we have easy access

Representative Sample

Members of the population that end up in our sample are likely to be similar to the population as a whole

Data set

Values of a number of variables, for the individuals in a sample

Continous variable

Takes on any numerical value

Discrete variable

Takes only certain values, no in between

3 measurement scales:

Ordinal, interval, ratio

Ordinal

The order of values can be given a meaningful interpretation (ex. unhappy, ok, happy survey)

Interval

The interval between values can be given a meaningful interpretation (ex. temperature)

Ratio

The ratio of values can be given a meaningful interpretation (ex. Money in pocket) (think true zero)

Distribution of a variable

The values that the variable has and the frequency with which each of these values occur

Histogram

Divides up range of the variable into bins of equal size, counts how many individuals are in each bin, uses heights of vertical bars to represent these values, bars always touch

Varience

How spread out the values are

Standard Deviation

Square root of variance- measure of how far the typical value is from the mean

Spread of distribution

Large SD

tightly bunches distribution

Small SD

Frequentist view

The probability of an event is proportion of times that this event would happen, out of all the times it could have happened

Proportion/ probability

restricted to range between 0 and 1

Z score

How far a value is from the mean in SD units

z- score equation

z= x- mean/SD