Problem Statement
The median of a distribution of 60 observations is 28.5. Find $x$ and $y$:
$\begin{array}{|c|c|c|c|c|c|c|} \hline \text{Class} & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 \\ \hline f & 5 & x & 20 & 15 & y & 5 \\ \hline \end{array}$
Verified Solution & Marking Scheme
Sum of Frequencies
$5 + x + 20 + 15 + y + 5 = 60 \implies x + y + 45 = 60 \implies x + y = 15$.
Identify Median Class
Median $28.5$ lies in $20 - 30$. $L = 20, f = 20, cf = 5 + x, h = 10, N/2 = 30$.
Apply Median Formula
$28.5 = 20 + \frac{30 - (5 + x)}{20} \times 10 \implies 8.5 = \frac{25 - x}{2} \implies 17 = 25 - x \implies x = 8$
$y = 15 - 8 = 7$.