# Statistics Random Data And Numerical Data

### Statistics Random Data And Numerical Data

This Statistics chapter is about random data and numerical data.

statistics

a branch of mathematics dealing with the collection, analysis, interpretation and presentation of masses of numerical data

descriptive statistics

organizes, presents, summarizes: graphically, numerically, pictorially..convenient and informative, simplifies comparisons

Inferential

estimates, predicts, decides, draw conclusions or inferences, USES SMALLER AMOUNTS OF DATA

population

is the group (individuals,items, measurements) of interest which is usually not easy to access directly

paramater

describes some characteristics of the population. paramaters are usually unknown

sample

a part of the population that we actually examine and for which we collect data. it is smaller (sometimes more accessible) group

statistic

is a number that describes a characteristic of a sample. often, a sample is used to estimate an unknown parameter

statistical inference

the process of making an estimate, prediction, or decision about a population based on a sample

confidence levels

tells the proportion of time that our conclusion will be correct

significance levels

a numerical measure of how often a result will be wrong

variable

a characteristic of a population or sample of interest
interval
nominal
ordinal

interval

real numbers..heights weights prices- quantitative or numerical histograms

nominal

qualitative or categorical. the values of nominal data are categories. ex: single=1 married=2 pie charts and bar graphs

ordinal

values have an order a ranking to them. order is maintained no matter what numeric values are assigned.

bar chart

used to display frequencies
the bar represents each category, height of the bar represents the frequency
the base of the bar is arbitrary

pie chart

shows relative frequencies. the pies represent categories.

histogram stem and leaf and ogive

are used when the data is interval

contingency table

used to describe the relationship between two nominal variables. lists the frequencies of each combination of the values of the two variables. the data can then be summarized in a bar cart graphically

two interval variables related?

scatter diagram or scatterplot

independent variable

predictor, explanatory- stays the same. is labeled x on the horizontal axis

dependent variable

is the outcome or the response and is labeled y on the vertical axis

one nominal and one interval

bar chart is an effective way to summarize this.

time series plot

observations measured at successive points in time.graphed on a line chart. time periods go on the horizontal axis

mean

average. appropriate for describing interval data.

x-bar

mean for a sample

mu

mean for a population

median

appropriate for interval or ordinal data. best for data dealing with extreme values. computed the same for population and sample. (n+1)/2

mode

occurs most frequently. useful for all data mainly for identifying the group with the highest frequency for nominal data

geometric mean

used when the variable is a growth rate of change.

range

largest observation-smallest observation

variance

population- sigma squared
sample s^2

standard deviation

square root of the variance

Cross-sectional data

data that is collected at a certain point in time. starting salaries of mba students.

longitudinal data

is collected over a period of time. weekly starting prices of gold.

prospective

collected from the current point in the future

retrospective or historical

collected on events that have happened in the past.

sampling

the process of selecting a subset of a whole population. cost efficient. and practical. the sample and the target population should be similar to each other.

sampling plan.

a method or procedure for specifying how a sample will be taken from a population.
simple random
stratified random
cluster sampling

simple random

everyone has an equal chance of being selected

stratified random

separating the population into mutually exclusive set. split into groups first and then use random sampling

cluster sample

a simple random sample of groups or clusters. may increase error

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