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Original
2026-01-01
Modified
2026-02-28
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<p>Median works for both ungrouped lists and class-interval data. Ungrouped data uses the middle number, but grouped data requires a frequency-based formula.</p>
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<p>Median works for both ungrouped lists and class-interval data. Ungrouped data uses the middle number, but grouped data requires a frequency-based formula.</p>
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<p><strong>Grouped Data:</strong> In grouped data, the information is arranged in class intervals with their frequencies and cumulative frequencies. The median is then found using this Formula: </p>
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<p><strong>Grouped Data:</strong> In grouped data, the information is arranged in class intervals with their frequencies and cumulative frequencies. The median is then found using this Formula: </p>
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<p>Median = \(l + \frac{\left(\frac{n}{2} - \text{cf}\right)}{f} \times h\)</p>
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<p>Median = \(l + \frac{\left(\frac{n}{2} - \text{cf}\right)}{f} \times h\)</p>
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<p>Where:</p>
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<p>Where:</p>
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<p>l = lower limit of the median class</p>
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<p>l = lower limit of the median class</p>
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<p>n = total number of observations</p>
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<p>n = total number of observations</p>
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<p>f = frequency of the median class</p>
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<p>f = frequency of the median class</p>
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<p>h = class size (class width)</p>
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<p>h = class size (class width)</p>
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<p>cf =<a>cumulative frequency</a>of the class just before the median class</p>
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<p>cf =<a>cumulative frequency</a>of the class just before the median class</p>
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<p>For example, find the median of the following data:</p>
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<p>For example, find the median of the following data:</p>
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<p><strong>Step 2:</strong>Total observations n = 50</p>
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<p><strong>Step 2:</strong>Total observations n = 50</p>
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<p><strong>Step 3:</strong>Find \(\frac{n}{2} = \frac{50}{2} = 25\)</p>
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<p><strong>Step 3:</strong>Find \(\frac{n}{2} = \frac{50}{2} = 25\)</p>
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<p>Locate the class where CF ≥ 25 → Median Class = 20-30</p>
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<p>Locate the class where CF ≥ 25 → Median Class = 20-30</p>
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<p><strong>Step 4:</strong>Apply the Formula</p>
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<p><strong>Step 4:</strong>Apply the Formula</p>
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<p>l = 20 f = 14 cf = 14 (CF before median class) h = 10</p>
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<p>l = 20 f = 14 cf = 14 (CF before median class) h = 10</p>
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<p>Median = \(20 + \left( \frac{25 - 14}{14} \right) \times 10\) =\(20 + \left( \frac{11}{14} \right) \times 10\)</p>
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<p>Median = \(20 + \left( \frac{25 - 14}{14} \right) \times 10\) =\(20 + \left( \frac{11}{14} \right) \times 10\)</p>
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<p>\(= 20 + 7.86 = 27.86\)</p>
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<p>\(= 20 + 7.86 = 27.86\)</p>
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<p>Median ≈ 27.86.</p>
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<p>Median ≈ 27.86.</p>
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<p><strong>Ungrouped Data:</strong>In ungrouped data, the information is listed as individual values rather than the class intervals. To find the median, the data is first arranged in<a>ascending order</a>, and then the median formula is applied depending on whether the number of observations (n) is odd or even.</p>
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<p><strong>Ungrouped Data:</strong>In ungrouped data, the information is listed as individual values rather than the class intervals. To find the median, the data is first arranged in<a>ascending order</a>, and then the median formula is applied depending on whether the number of observations (n) is odd or even.</p>
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<p><strong>Median of Ungrouped Data: </strong>Ungrouped data means that the numbers are listed individually, without grouping them into intervals. The way we find the median depends on whether n is odd or even.</p>
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<p><strong>Median of Ungrouped Data: </strong>Ungrouped data means that the numbers are listed individually, without grouping them into intervals. The way we find the median depends on whether n is odd or even.</p>
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<p>Median Formula When n Is Odd</p>
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<p>Median Formula When n Is Odd</p>
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<p>If the number of values is odd:</p>
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<p>If the number of values is odd:</p>
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<p>Median = \(\left( \frac{n + 1}{2} \right)^{\text{th}} \text{ value}\)</p>
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<p>Median = \(\left( \frac{n + 1}{2} \right)^{\text{th}} \text{ value}\)</p>
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<p><strong>Example (Odd Number of Values)</strong></p>
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<p><strong>Example (Odd Number of Values)</strong></p>
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<p>Find the median of 12, 18, 25, 30, 45</p>
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<p>Find the median of 12, 18, 25, 30, 45</p>
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<p>Arrange in order → already sorted.</p>
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<p>Arrange in order → already sorted.</p>
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<p>Number of values = 5 (odd)</p>
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<p>Number of values = 5 (odd)</p>
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<p>Median = \(\frac{5 + 1}{2}\) = 3rd value</p>
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<p>Median = \(\frac{5 + 1}{2}\) = 3rd value</p>
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<p>The 3rd value is 25</p>
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<p>The 3rd value is 25</p>
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<p> Median = 25</p>
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<p> Median = 25</p>
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<p><strong>Median Formula When n Is Even</strong></p>
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<p><strong>Median Formula When n Is Even</strong></p>
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<p>If the number of values is even:</p>
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<p>If the number of values is even:</p>
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<p>Median =\(\left( \frac{n + 1}{2} \right)^{\text{th}} \text{ value}\)</p>
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<p>Median =\(\left( \frac{n + 1}{2} \right)^{\text{th}} \text{ value}\)</p>
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<p><strong>Example (Even Number of Values)</strong></p>
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<p><strong>Example (Even Number of Values)</strong></p>
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<p>Find the median of: \(10, 15, 20, 30, 40, 55\)</p>
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<p>Find the median of: \(10, 15, 20, 30, 40, 55\)</p>
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<p>Arrange in order is already sorted.</p>
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<p>Arrange in order is already sorted.</p>
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<p>Number of values = 6 (even)</p>
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<p>Number of values = 6 (even)</p>
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<p>Middle values = 3rd (20) and 4th (30)</p>
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<p>Middle values = 3rd (20) and 4th (30)</p>
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<p>Median = \(\frac{20 + 30}{2}\)</p>
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<p>Median = \(\frac{20 + 30}{2}\)</p>
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<p>Median = 25</p>
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<p>Median = 25</p>