Statistics
Analysis of Frequency Distributions
Grade 11
Question:
<p>If in a frequently distribution, the mean and median are 21 and 22, respectively, then its mode is, approximately,</p>
<p>22.0</p>
<p>20.5</p>
<p>25.5</p>
<p>24.0</p>
Step-by-Step Solution
Key Concept: Use the empirical relationship between mean, median, and mode for moderately skewed distributions: Mode ≈ 3(Median) - 2(Mean). This relationship holds when data is approximately normally distributed with slight skewness.
<p><strong>Step 1:</strong> Identify given information</p><p>Mean = 21, Median = 22</p><p><strong>Step 2:</strong> Apply the empirical relationship for skewed distributions</p><p>For moderately skewed (non-normal) distributions, the relationship is:</p><p><strong>Mode ≈ 3(Median) - 2(Mean)</strong></p><p><strong>Step 3:</strong> Calculate the mode</p><p>Mode ≈ 3(22) - 2(21)</p><p>Mode ≈ 66 - 42</p><p>Mode ≈ 24</p><p><strong>Step 4:</strong> Verify reasonableness</p><p>Since Mean (21) < Median (22) < Mode (24), this indicates a negatively skewed distribution, which is consistent with the given values.</p><p><strong>∴ Answer: D (Mode ≈ 24)</strong></p>
Correct Answer: D