\documentclass[10pt, aspectratio=169]{beamer}
\usepackage[applemac]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usetheme{Madrid}
\usepackage{ragged2e}
\usepackage{graphicx}
\begin{document}
\author{Bindeshwar Singh Kushwaha}
\title{Question Based on Variance}
\subtitle{Data Science and A.I. Lecture Series}
\logo{“D:/PostNetwork Academy/logo.png”}
\institute{PostNetwork Academy}
%\subject{}
%\setbeamercovered{transparent}
%\setbeamertemplate{navigation symbols}{}
\date{}
\begin{frame}[plain]
\maketitle
\end{frame}
\begin{frame}{Reach PostNetwork Academy}
\begin{block}{Website}
PostNetwork Academy | www.postnetwork.co\\
\end{block}
\begin{block}{YouTube Channel}
www.youtube.com/@postnetworkacademy
\end{block}
\begin{block}{ PostNetwork Academy Facebook Page}
www.facebook.com/postnetworkacademy
\end{block}
\begin{block}{LinkedIn}
www.linkedin.com/company/postnetworkacademy
\end{block}
\end{frame}
\begin{frame}
\begin{block}{GitHub}
GitHub|
www.github.com/postnetworkacademy
\end{block}
\begin{block}{GeoGebra}
GeoGebra|
www.geogebra.org/u/postnetworkacademy
\end{block}
\begin{block}{Telegram}
Telegram Channel|
www.t.me/postnetworkacademy
\end{block}
\begin{block}{Whatsapp Channel}
www.whatsapp.com/channel/0029VaEbbm97tkj9WCh8C03d
\end{block}
\end{frame}
\begin{frame}
\begin{block}{}
{\small If $x_i$ are observations and $f_i$ are frequencies of observations then variance is $Var(X)=\frac{1}{N} \sum_{i=1}^n f_i(x_i-\bar{X})^2=\frac{1}{N} {(\sum_{i=1}^n f_i x_i^2)-\bar{X}^2}$}
\end{block}
\begin{columns}[T,onlytextwidth]
\column{0.25\textwidth}
\begin{block}{}
\uncover<2->{{\small $Var(X)=\frac{1}{N} \sum_{i=1}^n f_i(x_i-\bar{X})^2$}}
\end{block}
\begin{block}{}
\uncover<3->{{\small $=\frac{1}{N} \sum_{i=1}^n f_i(x_i^2+ \bar{X}^2-2 x_i\bar{X})$}}
\end{block}
\begin{block}{}
\uncover<4->{{\small $=\frac{1}{N} (\sum_{i=1}^n f_i x_i^2)-2 \bar{X}(\frac{1}{N} \sum_{i=1}^n f_i x_i)+\frac{N\bar{X}^2}{N}$}}
\end{block}
\begin{block}{}
\uncover<5->{{\small $=\frac{1}{N} (\sum_{i=1}^n f_i x_i^2)-2\bar{X}^2+\bar{X}^2$}}
\end{block}
\begin{block}{}
\uncover<6->{{\small $=\frac{1}{N} {(\sum_{i=1}^n f_i x_i^2)-\bar{X}^2}$}}
\end{block}
\column{0.70\textwidth}
\uncover<7->{{\scriptsize \begin{tabular}{|c|c|c|c|c|c|}
\hline
$x_i$&$f_i$& $f_i$$x_i$ & $x_i-\bar{X}$ & $(x_i-\bar{X})^2$& $f_i(x_i-\bar{X})^2$ \\
\hline
2 & 4& \uncover<9->{8} & \uncover<17-> {-7} &\uncover<25-> {49} &\uncover<33-> {196} \\
\hline
4& 4& \uncover<10->{16} & \uncover<18->{-5} &\uncover<26-> {25} & \uncover<34-> {100}\\
\hline
6 &5&\uncover<11->{30} &\uncover<19->{-3} &\uncover<27-> {9} &\uncover<35-> {45} \\
\hline
8 &15& \uncover<12->{120} &\uncover<20->{-1} &\uncover<28-> {1} &\uncover<36-> {15} \\
\hline
10&8& \uncover<13->{80} & \uncover<21->{1} & \uncover<29-> {1}& \uncover<37-> {8}\\
\hline
12& 5&\uncover<14->{60} &\uncover<22->{3} &\uncover<30-> {9} & \uncover<38-> {45}\\
\hline
14 &4& \uncover<14->{56} & \uncover<23->{5} &\uncover<31-> {25} &\uncover<39-> {100} \\
\hline
16 &5&\uncover<15->{80} & \uncover<24->{7} &\uncover<32-> {49} &\uncover<40-> {245} \\
\hline
& \uncover<8-> {N=50} & \uncover<15->{ $\sum_{i=1}^n f_i x_i=450$} & & & \uncover<41->{ $\sum_{i=1}^n f_i(x_i-\bar{X})^2=754$} \\
\hline
\end{tabular}}}
\uncover<16->{$\bar{X}=\frac{1}{N} \sum_{i=1}^n f_i x_i=\frac{450}{50}=9$}\\
\uncover<43->{$Var(X)=\frac{1}{N} \sum_{i=1}^n f_i(x_i-\bar{X})^2=\frac{754}{50}=15.5$}
\end{columns}
\end{frame}
\end{document}
This LaTeX code creates a presentation using the Beamer class, specifically tailored for discussing the concept of variance within the context of a Data Science and AI lecture series. Here’s a breakdown of what each section of the code does:
Document Setup
Document Class: `\documentclass[10pt, aspectratio=169]{beamer}`
Specifies a Beamer presentation with a font size of 10pt and a 16:9 aspect ratio.
Packages
`\usepackage[applemac]{inputenc}`: Supports input encoding for Mac.
`\usepackage[T1]{fontenc}`: Ensures proper font encoding.
`\usepackage{lmodern}`: Uses the Latin Modern font family for better aesthetics.
`\usetheme{Madrid}`: Chooses the Madrid theme for the presentation.
`\usepackage{ragged2e}`: Allows for ragged-right text alignment.
`\usepackage{graphicx}`: Enables the inclusion of images.
Content of the Presentation
– Author Information:
– The author is named “Bindeshwar Singh Kushwaha.”
– The title is “Question Based on Variance,” and the subtitle indicates it is part of a lecture series on Data Science and AI.
– The logo is specified (though the path may need adjustment).
– Frames: The presentation consists of multiple frames (slides):
1. Title Slide: Displays the title, author, and other introductory information.
2. Contact Information: Contains blocks of text with links to the PostNetwork Academy’s website, YouTube channel, Facebook page, and LinkedIn profile.
3. Further Resources: Lists additional resources like GitHub, GeoGebra, Telegram, and WhatsApp channels.
4. Variance Explanation:
– Introduces the formula for variance, explaining the relationship between observations and their frequencies.
– Breaks down the calculation of variance step-by-step, using a tabular format to illustrate the values of \(x_i\), \(f_i\), and their respective calculations.
– Provides detailed calculations and the final variance result.
Interactive Elements
– Uncover Command:
– `\uncover<2->` and similar commands reveal specific content progressively during the presentation, making it more engaging.
Mathematical Presentation
– Uses LaTeX math mode to display equations clearly, showing the derivation of variance and including a data table with calculations.
Conclusion
This LaTeX code creates a comprehensive and visually organized presentation on variance, ideal for an academic or professional setting focused on data science. The layout and theme choices enhance readability and engagement.
Output
varianceforfreqdist