Introduction to Statistics

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Liberty University's Dr. Moone's 1st quiz in class.

Plural

Statistics are numbers

Singular

Statistics is the study of data

Exploratory Statistics

The procedures used to organize and summarize numerical data

Inferential Statistics

The methods used to find out something about a population, based on a sample, generally we prefer to use a random sample for making inferences

Population

The set representing all measurements of interest to the researcher

Sample

Is a subset of measurements selected from the population of interest

Parameter

Refers to a quantity that characterizes a population.

Estimators

Refers to a quantity characterizes a sample.

X with a line on top

Sample Mean symbol

M

Population Mean symbol

N

Population symbol

Sample size

s2

Population Variance

s

Population Standard Deviation

Census

A sample consisting of the entire population

Constants

When observations on the same phenomenon do not change in successive trials, the phenomenon is called?

Variables

When observations on the same phenomenon vary from trial to trial, the phenomenon is called a?

Qualitative Variable

A variable whose observations vary in kind but not in degree

Quantitative Variable

A variable whose observations vary in magnitude from trial to trial

Nominal Level

A measurement that is used to refer to data that can only be classified into categories.

Ordinal Level

Observations are ordered or ranked

Interval Level

Observations ordered in such a way that distances between them are meaningful

Ration Level

Observations ordered in such a way that not only distances between them are meaningful but also ratios can be formed with levels of the scale

Statistics

A Collection of procedures and Principles for gaining and processing information in order to make decisions when faced with uncerntainty.

Bias

Does not represent the entire population fairly

Ratio

Result of one number or quantity divided by another

Proportion

a special type of ratio in which the denominator includes the numerator.

Percentage

The amount, number or rate of something, regarded as part of a total of 100

Rate

The occurrence of a particular outcome is found by dividing the actual number of occurrences by the number of possible outcomes.

Population Mean

Average of all individuals in the population

Sample mean

Average of all individuals in the sample

Pth Percentile

The distribution is the value such that p percent of observations fall at or below it

Outliers

Individual observations that fall well outside the overall pattern of data

Population Geometric Mean

a type of mean or average, which indicates the central tendency or typical value of a set of numbers.

Random

Any value which we cannot predict exactly

Random Process

Any experiment or process which produces some unpredictable or random values

Deterministic Process

Any experiment or process which produces values which can all be predicted exactly

Inference

Induction using data from a random process or experiment

Outcome

Each of the distinct results of an experiment

Sample Space

Set of all possible outcomes of an experiment

Event

A collection of outcome or subset of the sample space.

Mutually Exclusive

The occurrence of any one event means that none of the others can occur at the same time

u or

if two events A and B are not mutually exclusive

Law of multiplication

two events A, and B are independent if the occurrence of one event has no effect on the chance of occurrence of the other event.

Mutually Exclusive

_____ events cannot occur simultaneously

A or B

Venn- A, middle, B are shaded.

A and not B

Venn- only A is shaded without middle.

Not A and B

Venn- only B is shaded and not middle

not A

Venn- Everything but A and middle is shaded

Not B

Venn- Everything but B and middle is shaded

Not A and Not B

Venn- Only the outside is shaded

Not A or Not B

Venn- Everything but middle is shaded

Not A or B

Venn- Only outside is shaded this is a (or)

Not A and B

Venn- everthing but middle this is a (and)

Inferencial Statistics

What is the branch of statistics called for which we draw conclusions from sample data?

Nominal

Political Party Affiliation is an example of what level of measurement?

Ordinal

Categories of gross annual income: Superior/ good/ average/ poor isan example of what level of measurement?

P(A) + P(B)- P(A and B)= P(A or B)

Addition Law's equation if they are not mutually exclusive

P(A) + P(B)= P(A or B)

Addition Law's equation if they are Mutually exclusive

P(A) x P(B)= P(A and B)

Law of Multiplication equation

P(A l B) = P(A and B) / P(B)= P(A)

Conditional Probability's equation

Independent

With replacement of what is in the event

Dependent

Without Replacement of what is in the event

Discrete

The number of pencils produced daily (classify)

Continuous

The amount of rainfall in a month (classify)

Example: