FormulaHub/statistics.html at main · NawazHaider/FormulaHub · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
  <title>Chapter 13: Statistics</title>
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<body>
  <a href="index.html" class="back-button">
    <img src="https://copilot.microsoft.com/th/id/BCO.c46b5c8d-b20e-4d0d-bb65-8523ec478036.png" alt="Back" />
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  <div class="chapter-header" style="background-image: url('https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Histogram.svg/512px-Histogram.svg.png');">
    <h1>Chapter 13: Statistics – Formula Sheet</h1>
  </div>

  <div class="formula-box">
    <strong>Mean (Average):</strong>
    \( \bar{x} = \frac{\sum x_i}{n} \), where \( x_i \) are observations and \( n \) is the number of observations
  </div>

  <div class="formula-box">
    <strong>Mean of Grouped Data:</strong>
    \( \bar{x} = \frac{\sum f_i x_i}{\sum f_i} \), where \( f_i \) is frequency and \( x_i \) is mid-point
  </div>

  <div class="formula-box">
    <strong>Median (Grouped Data):</strong>
    \( \text{Median} = l + \left( \frac{\frac{n}{2} - F}{f} \right) \cdot h \)
    <br>Where:
    <ul>
      <li>\( l \) = lower boundary of median class</li>
      <li>\( F \) = cumulative frequency before median class</li>
      <li>\( f \) = frequency of median class</li>
      <li>\( h \) = class width</li>
    </ul>
  </div>

  <div class="formula-box">
    <strong>Mode (Grouped Data):</strong>
    \( \text{Mode} = l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \cdot h \)
    <br>Where:
    <ul>
      <li>\( l \) = lower boundary of modal class</li>
      <li>\( f_1 \) = frequency of modal class</li>
      <li>\( f_0 \) = frequency before modal class</li>
      <li>\( f_2 \) = frequency after modal class</li>
      <li>\( h \) = class width</li>
    </ul>
  </div>

  <div class="formula-box">
    <strong>Variance:</strong>
    \( \sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n} \)
  </div>

  <div class="formula-box">
    <strong>Standard Deviation:</strong>
    \( \sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}} \)
  </div>
</body>
</html>