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MATH 1280: unit 1: Introduction to statistics

Definitions

  • science of statistics: deals with the collection, analysis, interpretation and presentation of data.
  • probability: study uncertainty, formalization and quantification of the notion of uncertainty, deals with the chance of event occurring.
  • population: entire collection of persons, things or objects under study.
  • sample: studying entire large populations is inefficient; a sample is a portion (or subset) of the entire population, this sample will be studied to gather information about the population.
  • statistic: a number that is a property of the sample.
  • parameter: a number that is a property of the population; a statistic of a sample is used to estimate a parameter of the population; the better the sample representing the entire population the more accurate the estimation of the parameter from the statistic.
  • average (mean): (sum) / (count)
  • portion: (count (size) of specific group) / (size of entire population or sample).

R programming language

  • R is object oriented;
  • <- is the assignment operator in R.
  • every variable is an object in R.

  • some R functions that are available in R shell:

    R function its action
    c(…args) combine all its args into one object
    table(object) prints a table that contains the frequency of each element in the object
    plot(table) plots the table content
    getwd() get the current working directory
    setwd(path) set current directory to the supplied path
    mean(object) calculates the mean of this object
    summary(object) find the most common stats calculations for this object such as: mean, median, 1,2,3rd Quarter ..
    save.image (filename.Rdata) saves the current workspace image into a workspace image file called filename.Rdata in the current working directory
    rm(list = ls()) clear session memory
    q() quits the shell
    load(filename.Rdata) loads values saved in a workspace image file.Rdata into session memory
    read.csv (filePath) reads csv file
    file.choose() opens a finder navigator to select a file
    read.table (filePath, headers, sep =”,”) same as read.csv()
    read.delim(filePath) reads tabular data from tab delimited .txt files
    View(object) open detailed description of the object in the view popup
    write.table (object, filename, separator) export object data into external file, filename contains the extension of the new file
    write.csv(…), write.csv2(…) as above, but only export csv files
    data.frame(tableObject = table(object)) attach table contents with their frequencies in a clear labeled way
    cumsum(sequenceOfNumbers) add to each number, its previous numbers. eg. cumsum(1,2,3) => 1, 3, 6 => 1, (1+2), (1+2+3)
    paste(…strings, sep=”“) concatenates strings based on the sep argument
    hist(numericSequence) generates a histogram from the supplied sequence
    sd(numericSequence) returns the standard deviation of the supplied sequence
    var(numericSequence) returns the standard variance of the supplied sequence

References