\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{Jianmin Feng (taotao)}
\pdfinfo{
  /Title (ap-stat-01-describe-data.pdf)
  /Creator (Cheatography)
  /Author (Jianmin Feng (taotao))
  /Subject (AP Stat 01 Describe Data Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{16630D}
\definecolor{LightBackground}{HTML}{F7FAF7}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{AP Stat 01 Describe Data Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Jianmin Feng (taotao)} via \textcolor{DarkBackground}{\uline{cheatography.com/79308/cs/20351/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Jianmin Feng (taotao) \\
  \uline{cheatography.com/taotao} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 17th December, 2019.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.04057 cm} x{2.93643 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Collect Data}}  \tn
% Row 0
\SetRowColor{LightBackground}
type of variable & categorical vs quantitative (continuous vs discrete) \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
type of descriptive  methods & tabular, graphic, Numberical \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Tabular & n, f, rf, 100rf,cf, rcf, 100rcf \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
graphical & relations: bar, pie, dot, stem leave, histogram, cumulative freq \tn 
% Row Count 10 (+ 3)
% Row 4
\SetRowColor{LightBackground}
numberic & precise/inference, dull, complicated \tn 
% Row Count 12 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.74195 cm} x{3.23505 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{graph the data}}  \tn
% Row 0
\SetRowColor{LightBackground}
qualitative & bar pie \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
quantitative & dot plot,stemplot; histogram,cumulatice freq charts, boxplot \tn 
% Row Count 4 (+ 3)
% Row 2
\SetRowColor{LightBackground}
Examining graph & center(mean,median,mode), spread (range, std, variance), shape (symmetric, skewed) \tn 
% Row Count 8 (+ 4)
% Row 3
\SetRowColor{white}
\seqsplit{pattern/deviations} & cluster/gap, outliers \tn 
% Row Count 10 (+ 2)
% Row 4
\SetRowColor{LightBackground}
dotplot & spread,shape,approx center \tn 
% Row Count 11 (+ 1)
% Row 5
\SetRowColor{white}
stemplot & shaped,spread, center \tn 
% Row Count 12 (+ 1)
% Row 6
\SetRowColor{LightBackground}
histograph & f vs rf, shape/center, large dataset, error bar for spread \tn 
% Row Count 15 (+ 3)
% Row 7
\SetRowColor{white}
cumulative freq charts & S shaped, T(skewed) shape, meaningful order \tn 
% Row Count 17 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Central tendency - mean, median, mode}}  \tn
% Row 0
\SetRowColor{LightBackground}
summering distribution & population/sample, center/spread/sape \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
mean & mu=population mean,X bar=sample mean \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
median & for skewed data, odd/even sample size \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
mode & number with highest freq \tn 
% Row Count 7 (+ 1)
% Row 4
\SetRowColor{LightBackground}
symmetrical & mean=median=mode \tn 
% Row Count 8 (+ 1)
% Row 5
\SetRowColor{white}
left skewed & mode\textgreater{}median\textgreater{}mean \tn 
% Row Count 9 (+ 1)
% Row 6
\SetRowColor{LightBackground}
right skewed & mode\textgreater{}mean\textgreater{}media \tn 
% Row Count 10 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.59264 cm} x{3.38436 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{variance/spread - range, IQR, STD}}  \tn
% Row 0
\SetRowColor{LightBackground}
variance & spread from mean \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
range & largest-smallest measurement, outliers affect \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
IQR & interquartile range, eg Q3-Q1, not affected by outliers, median / IQR \tn 
% Row Count 6 (+ 3)
% Row 3
\SetRowColor{white}
STD & standard deviation, square root of variance, outlier affect, \textgreater{}=0 \tn 
% Row Count 9 (+ 3)
% Row 4
\SetRowColor{LightBackground}
variance & average the square of deviation from mean \tn 
% Row Count 11 (+ 2)
% Row 5
\SetRowColor{white}
population variance & N, sigma, mu \tn 
% Row Count 13 (+ 2)
% Row 6
\SetRowColor{LightBackground}
sample variance & n-1, x bar, s \tn 
% Row Count 15 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{mean/STD, median/IQR}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{0.9954 cm} x{3.9816 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Position - quartile,percentile,standarded score}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{percentile} & order, divide into 100 equal parts, count kth perncentile Pk \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\seqsplit{quartile} & order, divide into 4 equal parts (median calc), count kth quartile Qk, P25=Q1, P50=Q2.. \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
z score & standardized score, (x-mean)/std, compare datasets with different scales, eg temperature in north vs south city \tn 
% Row Count 9 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.89126 cm} x{3.08574 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Graphing uni variant data}}  \tn
% Row 0
\SetRowColor{LightBackground}
graphical summaries & Y scale:misleading manipulation \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
box plots & box(Q2-Q3) and whiskers(lower Q1,upper Q4), whiskers \textless{}1.5IQR  (Q3-Q1), L=Q1-1.5IQR, U=Q3+1.5IQR. point \textgreater{}U or \textless{}L are outliers \tn 
% Row Count 8 (+ 6)
% Row 2
\SetRowColor{LightBackground}
 & based on position, identify outlier and general shape(skewed or not) \tn 
% Row Count 11 (+ 3)
% Row 3
\SetRowColor{white}
 & calc: Q1, Median, Q3, IQR, L, U \tn 
% Row Count 13 (+ 2)
% Row 4
\SetRowColor{LightBackground}
shift unit +a & (variance/spread) range, std,IQR not affected \tn 
% Row Count 15 (+ 2)
% Row 5
\SetRowColor{white}
enlarge or shrink unit,*b & all stat enlarged or shrinked \tn 
% Row Count 17 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Compare distributions & center, spread, shape \tn 
% Row Count 19 (+ 2)
% Row 7
\SetRowColor{white}
 & outerlier or unusual values,cluster/gap \tn 
% Row Count 21 (+ 2)
% Row 8
\SetRowColor{LightBackground}
 & context of the question \tn 
% Row Count 22 (+ 1)
% Row 9
\SetRowColor{white}
 & dot plot, stemplot, histogram, freq polygram \tn 
% Row Count 24 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Avoid simple list the stat ( center,std and shape), instead, make a clear comparative statement.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.04057 cm} x{2.93643 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Bivariant data}}  \tn
% Row 0
\SetRowColor{LightBackground}
Scatter plot & shape: linear, non-linear, no relation \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
 & direction: positive or negative linear relation \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
 & strength of linear relation: close to the line \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Numeric methods} \tn 
% Row Count 8 (+ 1)
% Row 4
\SetRowColor{LightBackground}
correlation coefficient & degree and direction of linear relation of two quantitative variables (x,y) \tn 
% Row Count 12 (+ 4)
% Row 5
\SetRowColor{white}
 & rho and r, {[}-1,+1{]} \tn 
% Row Count 13 (+ 1)
% Row 6
\SetRowColor{LightBackground}
 & 0, 0.1, 0.5,0.85,1 \tn 
% Row Count 14 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{least squares regression line} \tn 
% Row Count 15 (+ 1)
% Row 8
\SetRowColor{LightBackground}
formular & Y = a+ bX  +e \tn 
% Row Count 16 (+ 1)
% Row 9
\SetRowColor{white}
Y & dependent/response variable \tn 
% Row Count 18 (+ 2)
% Row 10
\SetRowColor{LightBackground}
x & \seqsplit{independent/explanatory} variable \tn 
% Row Count 20 (+ 2)
% Row 11
\SetRowColor{white}
a & y intercept of line \tn 
% Row Count 21 (+ 1)
% Row 12
\SetRowColor{LightBackground}
b & slope of the line \tn 
% Row Count 22 (+ 1)
% Row 13
\SetRowColor{white}
e & random error, residual error \tn 
% Row Count 24 (+ 2)
% Row 14
\SetRowColor{LightBackground}
predicted vaue & y hat \tn 
% Row Count 25 (+ 1)
% Row 15
\SetRowColor{white}
residual error & e \tn 
% Row Count 26 (+ 1)
% Row 16
\SetRowColor{LightBackground}
least square regression & minimize the sum of squares of residual error \tn 
% Row Count 28 (+ 2)
% Row 17
\SetRowColor{white}
 & line of best fit (X bar, Y bar), slope=r(Sy/Sx) \tn 
% Row Count 31 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{x{2.04057 cm} x{2.93643 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Bivariant data (cont)}}  \tn
% Row 18
\SetRowColor{LightBackground}
coefficient of determination & R squared, percent of variance of Y determined by variance X \tn 
% Row Count 3 (+ 3)
% Row 19
\SetRowColor{white}
 & {[}-1,+1{]} \tn 
% Row Count 4 (+ 1)
% Row 20
\SetRowColor{LightBackground}
influential point & point that affect the correlation efficient \tn 
% Row Count 6 (+ 2)
% Row 21
\SetRowColor{white}
Outlier & maybe influential point \tn 
% Row Count 7 (+ 1)
% Row 22
\SetRowColor{LightBackground}
residual plot & should be random, or else, fit is not the best \tn 
% Row Count 9 (+ 2)
% Row 23
\SetRowColor{white}
transformation to fit linear & log, sqrt,reciprocal,square,power \tn 
% Row Count 11 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{1 calc slope, intercept, write formula, plot the linear line \newline 2 make a prediction, calc residual error \newline 3 calc coefficient of determination r = SSxy/sqrt(SSxx * SSyy) \newline  \newline stat and interpretation}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.89126 cm} x{3.08574 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{categorical data}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{marginal and joint freq of two way tables} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\seqsplit{contingency(joint)} table & r*c \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
marginal & row col grant total \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{conditional relative frequency} \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
association & compare with row total * col total /grand total \tn 
% Row Count 7 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}