For what value of $x$, is the median of the following frequency distribution $34.5$?

| Class | $0$-$10$ | $10$-$20$ | $20$-$30$ | $30$-$40$ | $40$-$50$ | $50$-$60$ | $60$-$70$ |
|-------|----------|-

Question

For what value of $x$, is the median of the following frequency distribution $34.5$?

| Class | $0$-$10$ | $10$-$20$ | $20$-$30$ | $30$-$40$ | $40$-$50$ | $50$-$60$ | $60$-$70$ |
|-------|----------|-----------|-----------|-----------|-----------|-----------|----------|
| Frequency | $3$ | $5$ | $11$ | $10$ | $x$ | $3$ | $2$ |

Accepted Answer

Step 1: Median class is $30$-$40$.
Step 2: Cumulative frequencies: $3, 8, 19, 29, 29+x, 32+x, 34+x$. Here $N = 34 + x$, $l = 30$, $f = 10$, $cf = 19$, $h = 10$.
Step 3: $34.5 = 30 + \frac{10}{10}\left(\frac{34 + x}{2} - 19\right) = 30 + \frac{34 + x}{2} - 19$
Step 4: $\Rightarrow 4.5 = \frac{34 + x}{2} - 19 \Rightarrow \frac{34 + x}{2} = 23.5 \Rightarrow 34 + x = 47 \Rightarrow x = 13$

Question

Solution