Statistics
Mode, Median, Mean Relation
Grade 11
Question:
<p>For a slightly asymmetric distribution, mean and median are 5 and 6, respectively. What is its mode?</p>
<p>5</p>
<p>6</p>
<p>7</p>
<p>8</p>
Step-by-Step Solution
Key Concept: For a slightly asymmetric (moderately skewed) distribution, use the empirical relationship: Mode = 3×Median - 2×Mean. This formula connects the three measures of central tendency when skewness is present.
<p><strong>Step 1:</strong> Identify the given data.<br/>Mean = 5, Median = 6</p><p><strong>Step 2:</strong> Apply the empirical relationship for asymmetric distributions.<br/>Mode = 3×Median - 2×Mean</p><p><strong>Step 3:</strong> Substitute the values.<br/>Mode = 3(6) - 2(5)<br/>Mode = 18 - 10<br/>Mode = 8</p><p><strong>Step 4:</strong> Verify using skewness.<br/>Since Mean < Median < Mode (5 < 6 < 8), the distribution is negatively skewed (left-skewed), which is consistent with a slightly asymmetric distribution.</p><p>∴ Answer: <strong>D (Mode = 8)</strong></p>
Correct Answer: D