Question

Mean and standard deviation of marks obtained in some particular subject by four classes are given below. Report the class with the best performance

• A. 80, 18
• B. 75, 5
• C. 80, 21
• D. 76, 7

Hint:

Best performance is judged by highest consistency: choose class with minimum coefficient of variation \(\frac{\sigma}{\mu}\).

Answer 1

The Correct Option is B

Step 1: Meaning of best performance.
Best performance means:
- High average (mean)
- Low variation (standard deviation)
Step 2: Compare coefficient of variation (CV).
\[ CV=\frac{\sigma}{\mu}\times 100 \]
Step 3: Compute CV for each class.
(A):
\[ CV=\frac{18}{80}\times 100=22.5% \]
(B):
\[ CV=\frac{5}{75}\times 100\approx 6.67% \]
(C):
\[ CV=\frac{21}{80}\times 100=26.25% \]
(D):
\[ CV=\frac{7}{76}\times 100\approx 9.21% \]
Step 4: Decide best class.
Lowest CV means most consistent performance.
Option (B) has lowest CV.
Final Answer:
\[ \boxed{\text{Class with mean }75\text{ and SD }5} \]