310 stats

midterm prep

descriptive statistics

Summarize and describe the important characteristics of a set of measurements in a clear way

inferrential statistics

make inferences about population characteristics from a sample

experimental unit

the individual or object on which a variable is measured

probability

the numerical measure of the likelihood that an event will occur

measurement/data value

when a variable is actually measured on an experimental unit

data

a set of measurements from observations, counts, measurements, or responses

sample

a subset or sub collection of measurements selected from the population

population

the set of all measurements of interest in the investigator

variables

a characteristics that changes or varies over time and/or for different individuals or objects under consideration

observations

values of characteristics that have been measured

dataset

a collection of observations on a group (sample) of entities

univariate data

one variable is measured on a single experimental unit

bivariate data

two variables are measured on a single experimental unit

multivariate data

more than two variables are measured on a single experimental unit

What are the types of data (variables)

Qualitative (categorical)

Quantitative (numerical)

• discrete

• continuous

Qualitative (categotical) variables

measures a quality or characteristic on each experimental unit which cannot be measured numerically: Ex. hair color

Quantitative (numerical) variables

measure a numerical quantity on each experimental unit

Discrete

Can be counted + can take on only particular value

Continuous

can be measured, can take on any value in an interval, could have any number of decimals

relative frequency histogram

a bar graph in which the heigh of the bar shows how often a measurement falls in a particular class or subinterval

What are numerical measures used for

populations and samples

what does a parameter measure

a numerical descriptive measure calculated for a population

what does a statistic measure

A numerical descriptive measure calculated for a sample

measure of center

A measure along the horizontal axis of the data distribution that locates the center of the distribution

how do you find the mean?

Take the average (sum of the measurements divided by the total number of measurements taken)

median

midpoint of ranked values

mode

the most frequently observed value

What is the position of the median?

.5(n+1) after measurements have been ordered (not affected by extreme outliers)

what does n represent

sample size

variance

the measure of variability of all points and measurements - based on deviations of points and measurements from their mean

the variance of a population

the average of the squared deviations of the measurements about their mean μ.

the variance of a sample

the sum of the squared deviations of the measurements about their mean, divided by (n-1)

standard deviation

The positive square root of the variance

measures of variability provide what

information on the spread or variability of the data values

Simple event

the outcome that is observed on a single repetition of the experiment

Sample space (S)

The set of all simple events of an experiment / aka the population

event

a collection of one or more simple events

Theoretical probability

Calculations based on theory where all possibilities are equally as likely

Empiricle probability

based on observation

permutation

an arrangement of items in a particular order

combination

a collection of data in which order does not matter

union

of A and B, is the event that either A or B or both occur when the experiment is performed

How is data generated

1. experimental units, variables, measurements

2. samples and populations

3. univariate, bivariate, and multivariate data

what type of chart do you use when at least one variable is qualitative

bar chart or comparative pie chart

what is 𝑆𝑥𝑦

covariance

what is s_x

standard deviation of x

what is s_y

standard deviation of y

y is the blank variable

dependent

x is the blank variable

independent

what is the regression line

the line you draw through data points to show the relationship between two variables

what is p(a)

probability of event a

how do you find p(a)

add together all probabilities of simple events in the space of a

theoretical probability

based on theory w/ outcomes that are equally likely

empirical probability

based on observations

what is the mn rule and what is it used for

If an experiment is performed in two stages, with m ways to accomplish the first stage and n ways to accomplish the second stage, then there are mn ways to accomplish the experiment - it is used to fidn the total number of simple events

describe permutations for ordering

the number of ways you can arrange n distinct objects, taking them r at a time

are there more combinations or permutations

permutations

what is A_c and what does it mean

the compliment of event a - all outcomes in an experiment that do not result in event a

what is a mutually exclusive event

when one event occurs, the other cannot

what does a z-score tell you

how many standard deviations you are away from the mean