Statistics
Mode, Median, Mean Relation
Grade 11
Question:
<p>In a moderately skewed distribution, the values of mean and median are 5 and 6, respectively. The value of mode in such a situation is approximately equal to</p>
<p>8</p>
<p>11</p>
<p>6</p>
<p>None of these</p>
Step-by-Step Solution
Key Concept: Use Pearson's empirical relationship for skewed distributions: Mode ≈ 3(Median) - 2(Mean). This relationship holds approximately for moderately skewed distributions and directly connects the three measures of central tendency.
<p><strong>Step 1:</strong> Identify the given information</p><p>Mean = 5, Median = 6</p><p>Distribution is moderately skewed</p><p><strong>Step 2:</strong> Apply Pearson's empirical relationship</p><p>For moderately skewed distributions:</p><p>Mode ≈ 3(Median) - 2(Mean)</p><p><strong>Step 3:</strong> Substitute values</p><p>Mode ≈ 3(6) - 2(5)</p><p>Mode ≈ 18 - 10</p><p>Mode ≈ 8</p><p><strong>Step 4:</strong> Interpret the result</p><p>Since Mean (5) < Median (6) < Mode (8), the distribution is negatively skewed (left-skewed), which is consistent with the given condition.</p><p>∴ <strong>Mode ≈ 8</strong></p>
Correct Answer: A