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<!DOCTYPE html>
<html lang="en">
<head>
<title>Statistic Formula</title>
<link rel="icon" type="image/x-icon" href="./assets/images/favicon.ico">
<link rel="manifest" href="./manifest.json">
<script defer src="katex/katex.min.js"></script>
<script defer src="katex/contrib/auto-render.min.js" onload="renderMathInElement(document.body);"></script>
<link href="katex/katex.min.css" rel="stylesheet">
<style>
@import url(./variable.css);
* {
font-family: "Jost", sans-serif;
background-color: #d5f1f5;
text-align: center;
}
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color: black;
background-color: var(--appblack);
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form {
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h4 {
font-size: 28px;
padding: 20px;
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color: hsl(229, 84%, 12%);
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table,
th,
td {
border: 1px solid black;
margin-left: auto;
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}
li {
font-size: 21px;
font-weight: var(--fw-8);
color: var(--oxford-blue);
line-height: 1.3;
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</style>
</head>
<body>
<div id="stats">
<br>
<div class="stopwrap">
<div class="coll">
<div class="left">
<h4>Statistics Formula Sheet</h4>
<table class="table table-bordered table-dark">
<tbody>
<tr>
<th scope="row">\[Mean\]</th>
<td>\[\bar{x}=\frac{\sum x}{n}\]</td>
<td>
<p>\[x\,=\, Observations \,given\]</p>
<p>\[n\, =\, Total\, number\, of\]</p>
<p>\[observations\]</p>
</td>
</tr>
<tr>
<th scope="row">\[Median\]</th>
<td>
<p>\[If\, n\, is\, odd,\, then\]</p>
<p>\[M\,=(\frac{n+1}{2})\,term\]</p>
<p>\[If\, n\, is\, even,\, then\]</p>
<p>\[M
\,=\,\frac{(\frac{n}{2})^{th}term+(\frac{n}{2}+1)^{th}term}{2}\]</p>
</td>
<td>
<p>\[n \,= \,Total\, number \,of\]</p>
<p> \[observations\]</p>
</td>
</tr>
<tr>
<th scope="row">\[Mode\]</th>
<td>
<p></p>\[The\, value\, which\, occurs\]</p>
<p>\[most\,
frequently\]</p>
</td>
<td>\[-\]</td>
</tr>
<tr>
<th scope="row">\[Variance\]</th>
<td>\[\sigma ^{2}\,=\,\frac{\sum (x-\bar{x})^{2}}{n}\]</td>
<td>
<p>\[x\, =\, Observations\, given\]</p>
<p>\[x¯\, =\, Mean\]</p>
<p>\[n \,= \,Total\, number \,of\]</p>
<p> \[observations\]</p>
</td>
</tr>
<tr>
<th scope="row">\[Standard \,Deviation\]</th>
<td>\[S = \sigma = \sqrt{\frac{\sum (x-\bar{x})^{2}}{n}}\]</td>
<td>
<p>\[x\, =\, Observations\, given\]</p>
<p>\[x¯\, =\, Mean\]</p>
<p>\[n \,= \,Total\, number \,of\]</p>
<p> \[observations\]</p>
</td>
</tr>
<tr>
<th scope="row">\[Range\]</th>
<td>\[L-S\]</td>
<td>
<p>\[L\, =\, Largest\, value\]</p>
<p>\[S\, =\, Smallest\, value\]</p>
</td>
</tr>
<tr>
<th scope="row">\[Coeff.\,of\,Range\]</th>
<td>\[\frac{L-S}{L+S}\]</td>
<td>
<p>\[L\, =\, Largest\, value\]</p>
<p>\[S\, =\, Smallest\, value\]</p>
</td>
</tr>
<tr>
<th scope="row">\[Coeff.\,of\,Variation\]</th>
<td>\[\frac{\sigma}{\bar{x}}*100\]</td>
<td>
<p>\[\sigma=Standard\, Deviation\]</p>
<p>\[x¯\, =\, Mean\]</p>
</td>
</tr>
<tr>
<th scope="row">\[Combined \,Mean\]</th>
<td>\[\frac{m\bar{x}\,+\,n\bar{y}}{m+n}\]</td>
<td>
<p>\[x¯\,/y¯\, =\, Mean\, of\, two\]</p>
<p>\[distributions\]</p>
<p>\[m\,/n\,=no.\,of\,elements\,in\,\]</p>
<p>\[each\,distributions\]</p>
</td>
</tr>
<tr>
<th scope="row">\[Weighted\,Mean\]</th>
<td>\[\frac{\sum Wi\,xi}{\sum Wi}\]</td>
<td>
<p>\[Wi=Weight \,of\, each\]</p>
<p>\[distributions\]</p>
<p>\[xi=ith\,observation\]</p>
</td>
</tr>
<tr>
<th scope="row">
<p>\[Mean\,Deviation\]</p>
<p>\[about\,mean\]</p>
<p>\[\bar{X}\]
</th>
<td>\[\frac{\sum|xi-\bar{x}|}{n}\]</td>
<td>
<p>\[n \,= \,Total\, number \,of\]</p>
<p> \[observations\]</p>
<p>\[x¯\, =\, Mean\]</p>
<p>\[xi=ith\,observation\]</p>
</td>
</tr>
<tr>
<th scope="row">
<p>\[Mean\,Deviation\]</p>
<p>\[about\,median\]</p>
<p>\[M\]
</th>
<td>\[\frac{\sum|xi-M|}{n}\]</td>
<td>
<p>\[n \,= \,Total\, number \,of\]</p>
<p> \[observations\]</p>
<p>\[M\, =\, Median\]</p>
<p>\[xi=ith\,observation\]</p>
</td>
</tr>
<tr>
<th scope="row">
<p>\[Mean\,Deviation\]</p>
<p>\[about\,mode\]</p>
<p>\[Z\]</p>
</th>
<td>\[\frac{\sum|xi-Z|}{n}\]</td>
<td>
<p>\[n \,= \,Total\, number \,of\]</p>
<p> \[observations\]</p>
<p>\[Z\, =\, Mode\]</p>
<p>\[xi=ith\,observation\]</p>
</td>
</tr>
<tr>
<th scope="row">
<p>\[Mean\,Deviation\]</p>
<p>\[about\,any\,no.\,'a'\]</p>
</th>
<td>\[\frac{\sum|xi-a|}{n}\]</td>
<td>
<p>\[n \,= \,Total\, number \,of\]</p>
<p> \[observations\]</p>
<p>\[xi=ith\,observation\]</p>
</td>
</tr>
<tr>
<th scope="row">
<p>\[For \,symmetrical \]</p>
<p>\[Distribution:\]</p>
</th>
<td>\[Mode\,=\,3Median\,-\,2Mean\]</td>
<td>\[-\]</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</body>
</html>