The mean and S.D. of the marks of 200 candidates were found to be 40 and 15 respectively. Later, it was discovered that a score of 40 was wrongly read as 50. The correct mean and S.D. respectively are
Options:
A . 14.98, 39.95
B . 39.95, 14.98
C . 39.95, 224.5
D . None the these
Answer: Option B : B Corrected∑x=40×200−50+40=7990 ∴Corrected¯¯¯x=7990200=39.95 ∑x2=n[σ2+¯¯¯x2]=200[152+402]=365000 Correct∑x2=365000−2500+1600=364100 ∴Correctedσ=√364100200−(39.95)2 =√(1820.5−1596)=√224.5=14.98.
