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% Document Info
\author{Ktroch}
\pdfinfo{
  /Title (stats-and-math-prep.pdf)
  /Creator (Cheatography)
  /Author (Ktroch)
  /Subject (STATS \& MATH Prep Cheat Sheet)
}

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% Header and Footer
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\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{STATS \& MATH Prep Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Ktroch} via \textcolor{DarkBackground}{\uline{cheatography.com/144298/cs/30968/}}}
\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}Ktroch \\
  \uline{cheatography.com/ktroch} \\
  \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 3rd March, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
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% www.emerson.emory.edu/services/latex/latex_169.html
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{BEDMAS}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{•  Brackets} \tn 
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Brackets}} {\emph{Operations within brackets should be done first}} {\emph{ if there is two sets of brackets, solve the inside brackets then the outside.}} \newline  {\bf{ {\emph{Exponents }}refer to squared numbers and squared roots}} - A number that amplifies another number   Ex: 3$^{\textrm{3}}$  OR  ∛}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.23579 cm} x{1.78503 cm} x{1.55618 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Calculator keys}}  \tn
% Row 0
\SetRowColor{LightBackground}
Squared   x\textasciicircum{}2\textasciicircum{} & Exponent   x\textasciicircum{}x\textasciicircum{} & Negative   ( - ) or \textasciicircum{}+\textasciicircum{}/- \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
square Root   √◻ & Root   {\emph{shift}} {\emph{+}} {\bf{x}}\textasciicircum{}◻\textasciicircum{} & Fractions - ▬/◻ \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{5.377cm}}{Brackets   {\bf{(}}   OR   {\bf{)}}} \tn 
% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{5.377cm}}{{\emph{ Buttons will vary depending on your calculator}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Squared Numbers and Square Roots}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Squared Numbers }} - Multiplying a number by itself \newline % Row Count 2 (+ 2)
{\bf{ Square Roots}} - Determining which number multiplied by itself equals the number under the square root sign.% Row Count 5 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fractions: Part of a whole.}}  \tn
% Row 0
\SetRowColor{LightBackground}
Numerator is the top number & Denominator is the bottom \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Multiplying}} Fractions\{\{nl\}\} multiply the numerators and then multiply the denominators , then simplify & {\bf{Dividing}}\{\{nl\}\} invert the second fraction and multiply. \tn 
% Row Count 8 (+ 6)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Adding/Subtracting}} Fractions \{\{nl\}\} If the denominator is the same , add or subtract the numerators. \{\{nl\}\} If the denominator is different then find the least common multiple between the denominators and use that for the denominator. \{\{nl\}\} Multiply both numerator and denominator by the value needed to obtain the common denominator.} \tn 
% Row Count 15 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\emph{ Denominator is how many there are as a whole. Numerator is how many there are FROM the denominator.}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.43873 cm} x{2.53827 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Probability}}  \tn
% Row 0
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Certain {\emph{1:1, 100\%, 1, 1/1}} chance & Likely {\emph{0\% and 100\%}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Unlikely {\emph{0 to 1}} & Impossible {\emph{ 0:1, 0\%, 0, 0/1}} chance \tn 
% Row Count 4 (+ 2)
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\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Formal probability rule: \{\{nl\}\} All range between 0 and 1 (or 0\% and 100\%) always}  \tn 
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\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Statistics}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Statistics}} To help find patterns and relationships in data.\{\{nl\}\} \newline % Row Count 2 (+ 2)
{\bf{Data}} Information with context\{\{nl\}\} \newline % Row Count 3 (+ 1)
{\bf{Quantitative Variable}} Results in numbers with units where taking an average makes sense. {\emph{Charts, graphs, plots}} {\bf{spread = smallest value to biggest value}} \{\{nl\}\} \newline % Row Count 7 (+ 4)
{\bf{Categorial Variables}} Results in information placed into groups or categories. ( the count ∻ the total * 100 = the \% \{\{nl\}\}% Row Count 10 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Integers}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Integers}}- are whole numbers {\emph{(not decimals)}}  positive, negative, or zero {\emph{Example}}: 4 , -7 , 0} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Integers on a number line}} The larger the number, positive or negative the {\bf{further}} it is away from zero.} \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Absolute value of a number}}: is the distance away from zero. To represent the absolute value of a number, you write it like this |5|} \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Adding}}\{\{nl\}\}{\emph{When you are adding {\bf{Positive}} integers you move {\bf{right}} on the number line.\{\{nl\}\} 3 + 4 = 7 ⇒ {\bf{3 →→→→ 7}} \{\{nl\}\}  }}When adding {\bf{Negative}} numbers , you move to the {\bf{left}} on the number line* \{\{nl\}\}   5+(-2) = 3 ⇒ {\bf{3←← 5}}} \tn 
% Row Count 14 (+ 6)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Subtracting}}\{\{nl\}\} Subtraction is opposite of addition. Subtract a positive number count to the {\bf{left}}. Subtract a negative number and count to the {\bf{right}}.} \tn 
% Row Count 18 (+ 4)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{ Multiplying \& Divinding}} \{\{nl\}\} 2 positive integers = A positive\{\{nl\}\} 2 negative integers = A positive.\{\{nl\}\} 2 integers with mixed signs = A negative.} \tn 
% Row Count 22 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Proportions and Ratios}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Ratio}}: A way to describe the relationship between two numbers. {\emph{ 2:1 OR 2 to 1}} \{\{nl\}\} \newline % Row Count 2 (+ 2)
{\bf{Proportions}} A way to describe the relationship between two numbers using a ratio or decimal. \{\{nl\}\} \newline % Row Count 5 (+ 3)
{\bf{Equivalent Ratios}} Look different but equal the same. {\emph{3:6=0.5  4/8 =0.5}}% Row Count 7 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.53827 cm} x{2.43873 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Scientific notation}}  \tn
% Row 0
\SetRowColor{LightBackground}
230000000.00 = 2.3 x 10\textasciicircum{}8\textasciicircum{} & .000000012 = 1.2 x 10\textasciicircum{}-8\textasciicircum{} \tn 
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Scientific notation is a way of writing really big or really small numbers Using the base number 10. When doing a small number the exponent is negative}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.53827 cm} x{2.43873 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Scientific notation}}  \tn
% Row 0
\SetRowColor{LightBackground}
230000000.00 = 2.3 x 10\textasciicircum{}8\textasciicircum{} & .000000012 = 1.2 x 10\textasciicircum{}-8\textasciicircum{} \tn 
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Scientific notation is a way of writing really big or really small numbers Using the base number 10. When doing a small number the exponent is negative}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Calculator}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/ktroch_1646170923_v4-460px-Use-a-Calculator-Step-7.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Use this question to see if your calculator follows the order of operations. \newline 25 - 3x6 = ? \newline If the answer 7, then it DOES follow the order of operations. \newline If the answer 132, then it does NOT.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Place Value}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Tens} \tn 
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Decimals}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Decimals are like fractions, they are part of a whole.} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{To turn a fraction into a decimal, divide the numerator by the denominator.} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{To turn a decimal in to a fraction, place the decimal over its place value and then simplify. (find the common denominator with factoring.)} \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Decimal Rounding : How many decimal points do you want to keep?\{\{nl\}\} Look at the number to the right of the value. \{\{nl\}\} If the number is less than 5 keep it and drop the rest to the right. \{\{nl\}\} If the number is greater than or equal to 5 then add 1 to the number and drop the remaining to the right.} \tn 
% Row Count 14 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Algebra Terms}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Letters are used to represent missing numbers in an equation.\{\{nl\}\} \newline % Row Count 2 (+ 2)
{\bf{Constants}} Are the numbers in the equation.\{\{nl\}\} \newline % Row Count 4 (+ 2)
{\bf{Variables}} Are the letters in the equation. \{\{nl\}\} \newline % Row Count 6 (+ 2)
{\bf{Coefficient}} A number that is directly followed by a variable.  Grouped like this we are to multiply \{\{nl\}\}% Row Count 9 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Mean and Median}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Mean}}\{\{nl\}\} Mean = Average, Add all values and then divide by the number of values. x or a y with a bar over it. & {\bf{y=∑y/n}} \tn 
% Row Count 6 (+ 6)
% Row 1
\SetRowColor{white}
{\bf{Median}}\{\{nl\}\} The center, equal amount of units on each side\{\{nl\}\} First sort smallest to biggest then use the formula, Odd Median=Middle value, in position. Even Median=Average of two middle numbers , average of values in position & {\bf{Odd (n+1/2)\{\{nl\}\} Even (n/2) and (n/2+1)}} \tn 
% Row Count 18 (+ 12)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}