Question

Marks obtained by 40 students in a short assessment are given below, where a and b are missing data. [4 MARKS]
$\begin{array}{cccccc}Marks& 5& 6& 7& 8& 9\\ Numberof& 6& a& 16& 13& b\\ Students& & & & & \end{array}$
If the mean of the distribution is 7.2, find a and b.

Answer 1

Formula: 2 Marks
Solution: 2 Marks

$\begin{array}{ccc}Marks& No.ofStudents& fx\\ \left(x\right)& \left(f\right)& \\ 5& 6& 30\\ 6& a& 6a\\ 7& 16& 112\\ 8& 13& 104\\ 9& b& 9b\\ & \sum f=40& \sum fx=246+6a\\ & =35+a+b& +9b\end{array}$
$\therefore$ Mean $=\frac{\sum fx}{\sum f}$
$\Rightarrow 7.2=\frac{246+6a+9b}{40}$
$\Rightarrow 246+6a+9b=288$
$\Rightarrow 6a+9b=42\dots \dots \left(i\right)$
Now 35 + a + b = 40
$\Rightarrow a+b=5\Rightarrow a=5-b$
From equation (i), we get
$6(5-b)+9b=42$
$\Rightarrow 3-6b+9b=42$
$\Rightarrow 3b=12\Rightarrow b=4$
Hence, a = 1 and b = 4