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% Document Info
\author{SarahLisaDance}
\pdfinfo{
  /Title (statistics-and-probability-unit-1.pdf)
  /Creator (Cheatography)
  /Author (SarahLisaDance)
  /Subject (Statistics and Probability Unit 1 Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Statistics and Probability Unit 1 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{SarahLisaDance} via \textcolor{DarkBackground}{\uline{cheatography.com/216217/cs/47198/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}SarahLisaDance \\
  \uline{cheatography.com/sarahlisadance} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 17th October, 2025.\\
   Updated 17th October, 2025.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{{\bf{1.1 Statistics: The Science and Art of Data}}}}  \tn
% Row 0
\SetRowColor{LightBackground}
Individuals & The person or thing described in the data set \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Variables & Any attribute for the individuals that can vary \{\{nl\}\} there are two types of variables \tn 
% Row Count 6 (+ 4)
% Row 2
\SetRowColor{LightBackground}
Categorical Variable & Has a label (favorite color) \tn 
% Row Count 8 (+ 2)
% Row 3
\SetRowColor{white}
Quantitative Variable & Numerical Value and makes sense to find an average (age) \tn 
% Row Count 11 (+ 3)
% Row 4
\SetRowColor{LightBackground}
Frequency table & Shows the count of each data point (Blue: 10) \tn 
% Row Count 13 (+ 2)
% Row 5
\SetRowColor{white}
Relative Frequency table & Shows the percentage of each data point. \tn 
% Row Count 15 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Percentage Formula & (Part/Whole)x100 \tn 
% Row Count 17 (+ 2)
% Row 7
\SetRowColor{white}
Dot Plots & Each dot reprecents one data point (don't skip values that don't have data points \tn 
% Row Count 21 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.72 cm} x{5.28 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{{\bf{1.3-4: Displaying Quantitative Data}}}}  \tn
% Row 0
\SetRowColor{LightBackground}
Skewed Left & The tail is on the left (more data is on the right) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Skewed Right & The tail is on the right (more data is on the left) \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Symmetrical & The data is split evenly (if you folded it, it would be similar) \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
Shape & Skewed left/right or symmetric \tn 
% Row Count 9 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Center & The typical value in the data set \tn 
% Row Count 11 (+ 2)
% Row 5
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Variability & How spread out the data is (Variability from \_\_ to \_\_) \tn 
% Row Count 14 (+ 3)
% Row 6
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Outliers & Values significantly far from the others \tn 
% Row Count 16 (+ 2)
% Row 7
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In context & Always connect the description to the actual scenario or context of the data \tn 
% Row Count 19 (+ 3)
% Row 8
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Described in context & The dot plot represents the number of books read last summer. The data is skewed to the right.  The center is around around 1-2 books read last summer. The number of books read varies from 0 to 9 books. There is an outlier of 9 books. \tn 
% Row Count 28 (+ 9)
% Row 9
\SetRowColor{white}
Stemplots & Stem and leaf plots organize quantitative data using the digits of the values \tn 
% Row Count 31 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{2.72 cm} x{5.28 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{{\bf{1.3-4: Displaying Quantitative Data}} (cont)}}  \tn
% Row 10
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Leaf & The last number/digit of the data point \tn 
% Row Count 2 (+ 2)
% Row 11
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Stem & the other numbers before the last number/digit \tn 
% Row Count 4 (+ 2)
% Row 12
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Split Stemplot & when each stem has too many data point the stems can be split in two: leaves 0-4 and leaves 5-9 \tn 
% Row Count 8 (+ 4)
% Row 13
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Info for stemplots & - Don't skip stems even if they don't have any leaves! \{\{nl\}\}- Always include a KEY!! \tn 
% Row Count 12 (+ 4)
% Row 14
\SetRowColor{LightBackground}
Back-to-Back Stemplot & To compare two groups of data you can create a stemplot with leaves on either side. The left represents one group of data and the other side represents the other group \tn 
% Row Count 19 (+ 7)
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{{\bf{1.7: Measuring Variability}}}}  \tn
% Row 0
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Standard Deviation (S\textasciitilde{}x\textasciitilde{}) & The average distance from the mean \tn 
% Row Count 2 (+ 2)
% Row 1
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Formula: S\textasciitilde{}x\textasciitilde{} & For the sake of your sanity PLEASE use your calculator \tn 
% Row Count 5 (+ 3)
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Interquartile Range (IQR) & The range of the middle 50\% of the data \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
Formula for IQR & IQR=Q\textasciitilde{}3\textasciitilde{}-Q\textasciitilde{}1\textasciitilde{} \tn 
% Row Count 8 (+ 1)
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% Row 0
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Bar Charts & each bar represents one category and the frequency or relative frequency (Helps compare data side by side) \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
Pie Chart & the circle represents the whole data set and each wedge represents the relative frequency of a category.  Represents data as a part of a whole \tn 
% Row Count 10 (+ 6)
% Row 2
\SetRowColor{LightBackground}
Deceptive graphs & Some representation of data are created to manipulate the perception of the data (Always check the scales on a chart and beware of pictographs) \tn 
% Row Count 16 (+ 6)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.28 cm} x{4.72 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{{\bf{1.5: Displaying Quantitative Data}}}}  \tn
% Row 0
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Step 1 & Divide your data into equal intervals \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Step 2 & Create a frequency table for each interval \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Step 3 & Label the axis. Label the horizontal axis with the intervals \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
Step 4 & Draw the bars for each interval. (no gaps) \tn 
% Row Count 9 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Notes on Histograms & The interval contains the first value but not the last \tn 
% Row Count 12 (+ 3)
% Row 5
\SetRowColor{white}
Relative Frequency histogram & - Use the same steps but with a relative frequency table \{\{nl\}\}- When made correctly, all the bars in a histogram should add up to 100\% or 1 \tn 
% Row Count 19 (+ 7)
% Row 6
\SetRowColor{LightBackground}
Shape & Skewed left/right or symmetric \tn 
% Row Count 21 (+ 2)
% Row 7
\SetRowColor{white}
Center & The typical interval in the data set \tn 
% Row Count 23 (+ 2)
% Row 8
\SetRowColor{LightBackground}
Variability & How spread out the data is \tn 
% Row Count 25 (+ 2)
% Row 9
\SetRowColor{white}
Outliers & intervals significantly far from the others \tn 
% Row Count 27 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{{\bf{1.6: Measuring Canter}}}}  \tn
% Row 0
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Mean & The average value of a data set \tn 
% Row Count 2 (+ 2)
% Row 1
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Median & The value in the middle of a data set \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Symmetric & Mean ≈ Median \{\{nl\}\}- use the mean for center \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
Skewed Right & Mean \textgreater{} Median \{\{nl\}\}- use the median for center \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Skewed Left & Mean \textless{} Median \{\{nl\}\}- use the median for center \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
Notes on Mean vs. Median & If there are outliers, use median for center since median is resistant to outliers. Mean is not resistant to outliers \tn 
% Row Count 15 (+ 5)
% Row 6
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Mode & The number that appears the most \tn 
% Row Count 17 (+ 2)
% Row 7
\SetRowColor{white}
Range & The difference between the highest and lowest data values \tn 
% Row Count 20 (+ 3)
% Row 8
\SetRowColor{LightBackground}
Quartiles & Dividing a data set into four intervals \tn 
% Row Count 22 (+ 2)
% Row 9
\SetRowColor{white}
First (Lower) Quartile & The middle of the lowerr half of the data set. The first quarter \tn 
% Row Count 25 (+ 3)
% Row 10
\SetRowColor{LightBackground}
Second Quartile (Median) & Middle Value. The second Quarter of half \tn 
% Row Count 27 (+ 2)
% Row 11
\SetRowColor{white}
Third (Upper) Quartile & Middle of the upper half of the data set. The third quarter \tn 
% Row Count 30 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{1.36 cm} x{6.64 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{{\bf{1.8: Boxplots and Outliers}}}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{Boxplots} & displays data using Min, Max, Q\textasciitilde{}1\textasciitilde{}, Q\textasciitilde{}3\textasciitilde{}, median, and outlier values \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
Step 1 & Create a numberline from the variability of the data \tn 
% Row Count 5 (+ 2)
% Row 2
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Step 2 & Make the Q1, Median, and Q3. draw a box between Q1 and Q3 with a line through the median \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
Step 3 & Mark the Min and Max (excluding the outlier values) and connect them to the box with a line \tn 
% Row Count 11 (+ 3)
% Row 4
\SetRowColor{LightBackground}
Step 4 & Add * to mark the high and low outliers \tn 
% Row Count 13 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}