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Override for the tutor's lesson content generation calls. Auto uses the system default (Claude Sonnet 5 for lesson text, Opus 5 for diagrams).

Lesson generation model

System default

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Tutoring abilities

Imagine three friends have 1 sticker, 2 stickers, and 6 stickers. How can we share them fairly so everyone has the exact same amount?

To describe any group of numbers, we use four helpful tools: **mean**, **median**, **mode**, and **range**.

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="aspect-ratio" content="4:3">
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    color: #1e2945;
    background: transparent;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100%;
    padding: 12px;
    user-select: none;
    -webkit-user-select: none;
  }

  .nav-tabs {
    display: flex;
    gap: 6px;
    background: #eef2f6;
    padding: 4px;
    border-radius: 10px;
    margin-bottom: 16px;
    max-width: 100%;
    flex-wrap: wrap;
    justify-content: center;
  }

  .tab-btn {
    border: none;
    background: transparent;
    padding: 6px 14px;
    font-size: 14px;
    font-weight: 600;
    color: #64748b;
    border-radius: 8px;
    cursor: pointer;
    transition: all 0.25s ease;
  }

  .tab-btn.active {
    background: #ffffff;
    color: #0284c7;
    box-shadow: 0 2px 6px rgba(0,0,0,0.08);
  }

  .stage {
    width: 100%;
    max-width: 440px;
    height: 220px;
    position: relative;
    display: flex;
    flex-direction: column;
    justify-content: flex-end;
    align-items: center;
    padding-bottom: 12px;
  }

  .bars-container {
    display: flex;
    align-items: flex-end;
    justify-content: center;
    gap: 8px;
    width: 100%;
    height: 160px;
    position: relative;
  }

  .col-item {
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: flex-end;
    flex: 1;
    max-width: 46px;
    height: 100%;
    position: relative;
    transition: transform 0.3s ease;
  }

  .bar {
    width: 100%;
    background: #cbd5e1;
    border-radius: 6px 6px 4px 4px;
    transition: all 0.35s ease;
    display: flex;
    align-items: flex-start;
    justify-content: center;
    padding-top: 4px;
    color: #ffffff;
    font-size: 13px;
    font-weight: 700;
  }

  .val-label {
    margin-top: 6px;
    font-size: 14px;
    font-weight: 700;
    color: #475569;
    transition: color 0.3s ease;
  }

  /* Overlays */
  .mean-line {
    position: absolute;
    left: 4%;
    right: 4%;
    bottom: calc(12px + (7 / 14) * 140px);
    height: 3px;
    background: #0284c7;
    border-radius: 2px;
    opacity: 0;
    transform: scaleX(0.2);
    transition: all 0.35s ease;
    pointer-events: none;
    z-index: 10;
  }

  .mean-tag {
    position: absolute;
    right: 0;
    top: -24px;
    background: #0284c7;
    color: #fff;
    font-size: 12px;
    font-weight: 700;
    padding: 2px 6px;
    border-radius: 4px;
    white-space: nowrap;
  }

  .range-span {
    position: absolute;
    bottom: 170px;
    left: 6%;
    right: 6%;
    height: 20px;
    display: flex;
    align-items: center;
    justify-content: space-between;
    opacity: 0;
    transition: opacity 0.35s ease;
  }

  .range-line {
    position: absolute;
    left: 0;
    right: 0;
    top: 50%;
    height: 2px;
    background: #8b5cf6;
    z-index: 1;
  }

  .range-tag {
    position: absolute;
    left: 50%;
    top: 50%;
    transform: translate(-50%, -50%);
    background: #8b5cf6;
    color: #fff;
    font-size: 12px;
    font-weight: 700;
    padding: 2px 8px;
    border-radius: 12px;
    z-index: 2;
    white-space: nowrap;
  }

  .arrow {
    width: 6px;
    height: 6px;
    border-top: 2px solid #8b5cf6;
    z-index: 2;
  }
  .arrow-left { border-left: 2px solid #8b5cf6; transform: rotate(-45deg); }
  .arrow-right { border-right: 2px solid #8b5cf6; transform: rotate(45deg); }

  /* Output calculation card */
  .formula-box {
    margin-top: 6px;
    min-height: 44px;
    display: flex;
    align-items: center;
    justify-content: center;
    font-size: 15px;
    font-weight: 600;
    color: #1e2945;
    background: #f1f5f9;
    padding: 8px 18px;
    border-radius: 8px;
    text-align: center;
  }

  .calc-sub {
    color: #64748b;
    font-size: 13px;
    margin-left: 6px;
    font-weight: 500;
  }

  /* Specific Highlight States */
  .highlight-mode {
    background: #f59e0b !important;
    box-shadow: 0 0 12px rgba(245, 158, 11, 0.45);
  }

  .highlight-median {
    background: #10b981 !important;
    box-shadow: 0 0 12px rgba(16, 185, 129, 0.45);
    transform: translateY(-4px);
  }

  .highlight-range {
    background: #8b5cf6 !important;
    box-shadow: 0 0 12px rgba(139, 92, 246, 0.45);
  }

  .highlight-mean {
    background: #0284c7 !important;
    opacity: 0.85;
  }

  .dim {
    opacity: 0.35;
  }
</style>
</head>
<body>

<div class="nav-tabs">
  <button class="tab-btn active" data-tool="mode">Mode</button>
  <button class="tab-btn" data-tool="median">Median</button>
  <button class="tab-btn" data-tool="range">Range</button>
  <button class="tab-btn" data-tool="mean">Mean</button>
</div>

<div class="stage">
  <div class="range-span" id="rangeSpan">
    <div class="arrow arrow-left"></div>
    <div class="range-line"></div>
    <div class="range-tag">14 − 3 = 11</div>
    <div class="arrow arrow-right"></div>
  </div>

  <div class="mean-line" id="meanLine">
    <div class="mean-tag">Mean = 7</div>
  </div>

  <div class="bars-container" id="barsContainer">
    
  </div>
</div>

<div class="formula-box" id="formulaBox">
  Mode: <strong>5</strong> <span class="calc-sub">(most frequent)</span>
</div>

<script>
  const data = [3, 5, 5, 5, 8, 9, 14];
  const maxVal = 14;
  const maxBarPx = 140;

  const container = document.getElementById('barsContainer');
  const meanLine = document.getElementById('meanLine');
  const rangeSpan = document.getElementById('rangeSpan');
  const formulaBox = document.getElementById('formulaBox');
  const tabs = document.querySelectorAll('.tab-btn');

  // Render bars
  data.forEach((v, idx) => {
    const col = document.createElement('div');
    col.className = 'col-item';
    col.id = `col-${idx}`;

    const bar = document.createElement('div');
    bar.className = 'bar';
    bar.style.height = `${(v / maxVal) * maxBarPx}px`;
    bar.textContent = v;

    const label = document.createElement('div');
    label.className = 'val-label';
    label.textContent = v;

    col.appendChild(bar);
    col.appendChild(label);
    container.appendChild(col);
  });

  const views = {
    mode: {
      update: () => {
        data.forEach((v, i) => {
          const b = document.querySelector(`#col-${i} .bar`);
          if (v === 5) {
            b.className = 'bar highlight-mode';
          } else {
            b.className = 'bar dim';
          }
        });
        meanLine.style.opacity = '0';
        meanLine.style.transform = 'scaleX(0.2)';
        rangeSpan.style.opacity = '0';
        formulaBox.innerHTML = 'Mode = <strong>5</strong> <span class="calc-sub">(most frequent, appears 3×)</span>';
      }
    },
    median: {
      update: () => {
        data.forEach((v, i) => {
          const b = document.querySelector(`#col-${i} .bar`);
          if (i === 3) {
            b.className = 'bar highlight-median';
          } else {
            b.className = 'bar dim';
          }
        });
        meanLine.style.opacity = '0';
        meanLine.style.transform = 'scaleX(0.2)';
        rangeSpan.style.opacity = '0';
        formulaBox.innerHTML = 'Median = <strong>5</strong> <span class="calc-sub">(middle value of sorted set)</span>';
      }
    },
    range: {
      update: () => {
        data.forEach((v, i) => {
          const b = document.querySelector(`#col-${i} .bar`);
          if (i === 0 || i === 6) {
            b.className = 'bar highlight-range';
          } else {
            b.className = 'bar dim';
          }
        });
        meanLine.style.opacity = '0';
        meanLine.style.transform = 'scaleX(0.2)';
        rangeSpan.style.opacity = '1';
        formulaBox.innerHTML = 'Range = <strong>11</strong> <span class="calc-sub">(14 − 3 = 11)</span>';
      }
    },
    mean: {
      update: () => {
        data.forEach((v, i) => {
          const b = document.querySelector(`#col-${i} .bar`);
          b.className = 'bar highlight-mean';
        });
        meanLine.style.opacity = '1';
        meanLine.style.transform = 'scaleX(1)';
        rangeSpan.style.opacity = '0';
        formulaBox.innerHTML = 'Mean = <strong>7</strong> <span class="calc-sub">(sum 49 ÷ 7 items)</span>';
      }
    }
  };

  function setView(name) {
    tabs.forEach(t => t.classList.toggle('active', t.dataset.tool === name));
    views[name].update();
  }

  tabs.forEach(btn => {
    btn.addEventListener('click', () => {
      setView(btn.dataset.tool);
    });
  });

  // Initial state
  views.mode.update();
</script>

</body>
</html>

Let's start with the easiest two to spot just by looking at your data.

The **mode** is the value that appears most often in a list. If every number appears only once, there is no mode.

The **range** shows how spread out the numbers are. You find it by subtracting the smallest value from the largest value.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Summary Statistics</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      padding: 12px;
    }

    .main-wrap {
      width: 100%;
      max-width: 520px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 16px;
    }

    /* Tabs */
    .tab-bar {
      display: flex;
      gap: 6px;
      background: #eef2f6;
      padding: 4px;
      border-radius: 10px;
      width: 100%;
      max-width: 440px;
    }

    .tab-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 8px 4px;
      font-size: 14px;
      font-weight: 600;
      color: #64748b;
      border-radius: 8px;
      cursor: pointer;
      transition: all 0.25s ease;
      text-align: center;
    }

    .tab-btn.active {
      background: #ffffff;
      color: #0284c7;
      box-shadow: 0 2px 6px rgba(0,0,0,0.08);
    }

    /* Data set display */
    .tiles-row {
      display: flex;
      justify-content: center;
      align-items: center;
      gap: 8px;
      width: 100%;
      padding: 8px 0;
      flex-wrap: nowrap;
    }

    .tile {
      width: 44px;
      height: 48px;
      border-radius: 10px;
      background: #ffffff;
      border: 2px solid #e2e8f0;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      font-size: 18px;
      font-weight: 700;
      color: #1e2945;
      transition: all 0.3s ease;
      position: relative;
    }

    .tile .tag {
      position: absolute;
      top: -10px;
      font-size: 9px;
      font-weight: 800;
      text-transform: uppercase;
      padding: 1px 4px;
      border-radius: 4px;
      opacity: 0;
      transform: translateY(3px);
      transition: all 0.25s ease;
      letter-spacing: 0.5px;
    }

    /* Tile states */
    .tile.highlight-blue {
      background: #e0f2fe;
      border-color: #0284c7;
      color: #0369a1;
      transform: translateY(-2px);
      box-shadow: 0 4px 10px rgba(2, 132, 199, 0.18);
    }
    .tile.highlight-blue .tag {
      opacity: 1;
      transform: translateY(0);
      background: #0284c7;
      color: #ffffff;
    }

    .tile.highlight-amber {
      background: #fef3c7;
      border-color: #d97706;
      color: #b45309;
      transform: translateY(-2px);
      box-shadow: 0 4px 10px rgba(217, 119, 6, 0.18);
    }
    .tile.highlight-amber .tag {
      opacity: 1;
      transform: translateY(0);
      background: #d97706;
      color: #ffffff;
    }

    .tile.highlight-green {
      background: #dcfce7;
      border-color: #16a34a;
      color: #15803d;
      transform: translateY(-2px);
      box-shadow: 0 4px 10px rgba(22, 163, 74, 0.18);
    }
    .tile.highlight-green .tag {
      opacity: 1;
      transform: translateY(0);
      background: #16a34a;
      color: #ffffff;
    }

    .tile.dimmed {
      opacity: 0.35;
      background: #f1f5f9;
      border-color: #cbd5e1;
    }

    /* Stage Presentation Box */
    .stage-card {
      width: 100%;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 16px 20px;
      min-height: 120px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      gap: 8px;
      box-shadow: 0 2px 8px rgba(0,0,0,0.04);
      text-align: center;
    }

    .calc-row {
      font-size: 20px;
      font-weight: 600;
      color: #334155;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      flex-wrap: wrap;
    }

    .calc-pill {
      display: inline-block;
      padding: 2px 8px;
      border-radius: 6px;
      font-weight: 700;
    }
    .pill-blue { background: #e0f2fe; color: #0284c7; }
    .pill-amber { background: #fef3c7; color: #b45309; }
    .pill-green { background: #dcfce7; color: #15803d; }

    .result-badge {
      font-size: 24px;
      font-weight: 800;
      color: #0f172a;
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .result-badge span {
      color: #0284c7;
    }

    /* Player controls */
    .controls {
      display: flex;
      align-items: center;
      gap: 12px;
    }

    .ctrl-btn {
      border: none;
      background: #f1f5f9;
      color: #475569;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 20px;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
      transition: background 0.2s;
    }
    .ctrl-btn:hover { background: #e2e8f0; }

    @media (max-width: 400px) {
      .tile {
        width: 36px;
        height: 42px;
        font-size: 15px;
      }
      .calc-row {
        font-size: 17px;
      }
      .result-badge {
        font-size: 20px;
      }
    }
  </style>
</head>
<body>

<div class="main-wrap">
  
  <div class="tab-bar">
    <button class="tab-btn active" onclick="setMode(0)">Range</button>
    <button class="tab-btn" onclick="setMode(1)">Median</button>
    <button class="tab-btn" onclick="setMode(2)">Mode</button>
    <button class="tab-btn" onclick="setMode(3)">Mean</button>
  </div>

  
  <div class="tiles-row" id="tilesRow">
    <div class="tile" id="t0"><span class="tag"></span>2</div>
    <div class="tile" id="t1"><span class="tag"></span>3</div>
    <div class="tile" id="t2"><span class="tag"></span>5</div>
    <div class="tile" id="t3"><span class="tag"></span>5</div>
    <div class="tile" id="t4"><span class="tag"></span>7</div>
    <div class="tile" id="t5"><span class="tag"></span>8</div>
    <div class="tile" id="t6"><span class="tag"></span>12</div>
  </div>

  
  <div class="stage-card" id="stageCard">
    
  </div>

  
  <div class="controls">
    <button class="ctrl-btn" id="playBtn" onclick="togglePlay()">
      <span id="playIcon">⏸</span> Auto
    </button>
  </div>
</div>

<script>
  const data = [2, 3, 5, 5, 7, 8, 12];
  let currentIdx = 0;
  let timer = null;
  let isPlaying = true;

  const views = [
    {
      name: "Range",
      renderTiles: () => {
        resetTiles();
        setTile(0, 'highlight-blue', 'Min');
        setTile(6, 'highlight-blue', 'Max');
        dimTiles([1, 2, 3, 4, 5]);
      },
      content: `
        <div class="calc-row">
          <span class="calc-pill pill-blue">12</span> − <span class="calc-pill pill-blue">2</span>
        </div>
        <div class="result-badge">Range = <span>10</span></div>
      `
    },
    {
      name: "Median",
      renderTiles: () => {
        resetTiles();
        dimTiles([0, 1, 2, 4, 5, 6]);
        setTile(3, 'highlight-amber', 'Mid');
      },
      content: `
        <div class="calc-row">
          Middle of ordered set
        </div>
        <div class="result-badge">Median = <span style="color:#d97706">5</span></div>
      `
    },
    {
      name: "Mode",
      renderTiles: () => {
        resetTiles();
        dimTiles([0, 1, 4, 5, 6]);
        setTile(2, 'highlight-green', '×2');
        setTile(3, 'highlight-green', '×2');
      },
      content: `
        <div class="calc-row">
          Most frequent value
        </div>
        <div class="result-badge">Mode = <span style="color:#16a34a">5</span></div>
      `
    },
    {
      name: "Mean",
      renderTiles: () => {
        resetTiles();
        for(let i = 0; i < 7; i++) {
          setTile(i, 'highlight-blue', '');
        }
      },
      content: `
        <div class="calc-row">
          (2 + 3 + 5 + 5 + 7 + 8 + 12) ÷ 7
        </div>
        <div class="result-badge">42 ÷ 7 = <span>6</span></div>
      `
    }
  ];

  function resetTiles() {
    for (let i = 0; i < 7; i++) {
      const el = document.getElementById('t' + i);
      el.className = 'tile';
      el.querySelector('.tag').textContent = '';
    }
  }

  function setTile(idx, cls, tagText) {
    const el = document.getElementById('t' + idx);
    el.classList.add(cls);
    if (tagText) {
      el.querySelector('.tag').textContent = tagText;
    }
  }

  function dimTiles(indices) {
    indices.forEach(i => {
      document.getElementById('t' + i).classList.add('dimmed');
    });
  }

  function setMode(idx) {
    currentIdx = idx;
    const tabs = document.querySelectorAll('.tab-btn');
    tabs.forEach((tab, i) => {
      tab.classList.toggle('active', i === idx);
    });

    const v = views[idx];
    v.renderTiles();
    document.getElementById('stageCard').innerHTML = v.content;
  }

  function nextStep() {
    currentIdx = (currentIdx + 1) % views.length;
    setMode(currentIdx);
  }

  function startAuto() {
    clearInterval(timer);
    timer = setInterval(nextStep, 3500);
    isPlaying = true;
    document.getElementById('playIcon').textContent = '⏸';
  }

  function pauseAuto() {
    clearInterval(timer);
    isPlaying = false;
    document.getElementById('playIcon').textContent = '▶';
  }

  function togglePlay() {
    if (isPlaying) {
      pauseAuto();
    } else {
      startAuto();
    }
  }

  // Initial load
  setMode(0);
  startAuto();
</script>

</body>
</html>

What happens if we want to find the number standing right in the center?

The **median** is the exact middle number when your data is arranged in order from least to greatest.

When you have an odd amount of numbers, you cross off pairs from both ends until only one middle number is left.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Finding the Median</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    }

    body {
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      padding: 16px;
      user-select: none;
    }

    .main-container {
      width: 100%;
      max-width: 580px;
      display: flex;
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      gap: 20px;
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    /* State badge / step title */
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      display: inline-flex;
      align-items: center;
      gap: 6px;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 20px;
      padding: 6px 14px;
      font-size: 14px;
      font-weight: 600;
      color: #475569;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
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    .status-badge .dot {
      width: 8px;
      height: 8px;
      border-radius: 50%;
      background: #22b7ff;
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    /* Board with number tiles */
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      display: flex;
      justify-content: center;
      align-items: center;
      gap: 8px;
      width: 100%;
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    .tile {
      width: 44px;
      height: 54px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
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      border: 2px solid #cbd5e1;
      border-radius: 10px;
      font-size: 22px;
      font-weight: 700;
      color: #1e2945;
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</head>
<body>

<div class="main-container">
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    <span class="dot"></span>
    <span id="step-label">Raw Data</span>
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</script>

</body>
</html>

A common mistake is picking the middle number before putting the list in order. Always sort your list first!

What happens if you have an even number of values, or numbers with decimals?

**Continuous data** includes measurements like race times or lengths that can take any decimal value, such as $1.5\text{ s}$, $2.0\text{ s}$, $2.5\text{ s}$, and $4.0\text{ s}$.

With an even count of numbers, two values share the middle. To find the median, find the halfway point by adding them and dividing by 2.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
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  <style>
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</head>
<body>

  <div class="stepper">
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    <button class="step-btn" id="btn-1" onclick="setStep(1)">2. Middle Pair</button>
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  <div class="stage">
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      <div class="tile" id="t5">18</div>
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    <div class="calc-area" id="calcArea"></div>
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      <span id="playIcon">⏸</span> Pause
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</body>
</html>

Now, how do we combine all these different values into one fair, balanced share?

The **mean** is the fair share value. You add all the numbers together, then divide by the total count of numbers.

For our four race times ($1.5$, $2.0$, $2.5$, and $4.0$), first add them up: $1.5 + 2.0 + 2.5 + 4.0 = 10.0$.

Next, divide that total by 4 because there are four times: $$10.0 \div 4 = 2.5\text{ s}$$

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Mean, Median, Mode, Range</title>
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Whenever you work with data, start by sorting your numbers from smallest to largest — it makes finding every measure fast and accurate!

math

Calculating the Mean, Median, Mode, and Range of Raw Data Sets. Calculate mean, median, mode, and range from lists of discrete and continuous numbers.

Averages and Spread - CfE Fourth Level / National 4 Mathematics

Summarizing Quantitative Data: Calculating and Comparing Mean, Median, Mode, and Range

Mean, Median, Mode and Range Textbook Exercises & Video Tutorials

To achieve mastery under Curriculum for Excellence MTH 4-20b, instruction must emphasize both procedural fluency (calculating averages and spread with integer and decimal values) and conceptual evaluation (interpreting data in real-life contexts). Teachers should explicitly present asymmetric distributions and skewed contexts (e.g., house prices, executive salaries) to challenge students to critique misleading statistics, choose the superior measure of central tendency, and justify their reasoning.

Calculating the Mean, Median, Mode, and Range of Raw Data Sets

Finding the Mode and Range

Finding the Median