<p>Consider the following statements:<br>(a) Mode can be computed from histogram.<br>(b) Median is not independent of change of scale.<br>(c) Variance is independent of change of origin and scale.</p>
Step-by-Step Solution
Key Concept: Understanding the properties of statistical measures: mode from histograms, median's dependence on scale, and variance's invariance to origin but not scale changes.
<p><strong>Step 1: Analyze Statement (a) - Mode from histogram</strong></p><p>Mode is the value with maximum frequency. In a histogram, the modal class is the one with the highest bar/frequency. The exact mode value can be estimated from the histogram using the modal class. <strong>Statement (a) is TRUE.</strong></p><p><strong>Step 2: Analyze Statement (b) - Median and change of scale</strong></p><p>If all observations are multiplied by a constant k (change of scale), the median also gets multiplied by k. For example, Median(2x₁, 2x₂, ...) = 2·Median(x₁, x₂, ...). Therefore, median is NOT independent of change of scale. <strong>Statement (b) is TRUE.</strong></p><p><strong>Step 3: Analyze Statement (c) - Variance and scale/origin</strong></p><p>Variance has these properties:</p><p>• Var(X + c) = Var(X) [independent of origin/shifting]</p><p>• Var(kX) = k²·Var(X) [dependent on scale - multiplied by square of scale factor]</p><p>Since variance changes with scale changes, it is NOT independent of scale. <strong>Statement (c) is FALSE.</strong></p><p><strong>Conclusion:</strong> Statements (a) and (b) are true; statement (c) is false.</p><p>∴ Answer: C</p>
Correct Answer: C