Question

The arithmetic mean of the scores of a group of students in a test was $52$ The brightest $20\%$ of them secured a mean score of $80$ and the dullest $25\%$ a mean score of $31$ The mean score of the remaining $55\%$ is

• A. $45\%$
• B. $50\%$
• C. $51.4\%$ (approx)
• D. $54.6\%$ (approx)

Answer 1

Answer: (C)

$51.4\%$ (approx)

Mean score of remaining $55\%$
$=\frac{[100\times 52-(20\times 80+25\times 31)]}{55}$

$=\frac{5200-(1600+775)}{55}$
$=\frac{5200-2375}{55}=\frac{2825}{55}=51.36\%$
$=51.4$