The median of the following data is $525$. Find the values of $x$ and $y$, if total frequency is $100$.

| Class | 0-100 | 100-200 | 200-300 | 300-400 | 400-500 | 500-600 | 600-700 | 700-800 | 800-900

Question

The median of the following data is $525$. Find the values of $x$ and $y$, if total frequency is $100$.

| Class | 0-100 | 100-200 | 200-300 | 300-400 | 400-500 | 500-600 | 600-700 | 700-800 | 800-900 | 900-1000 |
|---|---|---|---|---|---|---|---|---|---|---|
| Frequency | 2 | 5 | $x$ | 12 | 17 | 20 | $y$ | 9 | 7 | 4 |

Accepted Answer

Step 1: | Classes | Frequency | Cumulative Frequency |
|---|---|---|
| 0-100 | 2 | 2 |
| 100-200 | 5 | 7 |
| 200-300 | $x$ | $7+x$ |
| 300-400 | 12 | $19+x$ |
| 400-500 | 17 | $36+x$ |
| 500-600 | 20 | $56+x$ |
| 600-700 | $y$ | $56+x+y$ |
| 700-800 | 9 | $65+x+y$ |
| 800-900 | 7 | $72+x+y$ |
| 900-1000 | 4 | $76+x+y$ |
Step 2: $76 + x + y = 100 \Rightarrow x + y = 24$ ... (i)
$500 - 600$ is the median class.
Median $= 500 + \frac{50 - (36+x)}{20} 	imes 100 = 525$
Step 3: Solving we get, $x = 9$.
From (i), $y = 15$.

Question

Solution