Following data shows the information about marks obtained in Physics, Chemistry, Mathematics and Biology by 100 students in a class. Then subject shows the highest variability in marks. Choose the correct subject from the options below:
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To easily compare fractions like $\frac{4}{23}$ and $\frac{5}{27}$ without long division, cross-multiply their terms: $4 \times 27 = 108$ and $5 \times 23 = 115$. Since $115 \gt 108$, $\frac{5}{27}$ is larger, confirming Biology is more volatile than Math!
Step 1: Understanding the Question: We are given the mean and standard deviation of marks in four subjects and must determine which subject shows the highest relative variability.
Step 2: Key Formula or Approach: The Coefficient of Variation (C.V. = σ/μ) normalizes the standard deviation against the mean, allowing for fair comparison of dispersion across datasets with different averages.
Step 3: Detailed Explanation: Physics: 3/20 = 0.150; Chemistry: 2/25 = 0.080; Mathematics: 4/23 ≈ 0.174; Biology: 5/27 ≈ 0.185. Biology has the largest C.V., indicating the highest relative variability.
Step 4: Final Answer: The highest variability is in Biology, matching option (C).
