If mode of the following frequency distribution is $55$, then find the value of $x$.

| Class | $0$-$15$ | $15$-$30$ | $30$-$45$ | $45$-$60$ | $60$-$75$ | $75$-$90$ |
|-------|----------|-----------|-

Question

If mode of the following frequency distribution is $55$, then find the value of $x$.

| Class | $0$-$15$ | $15$-$30$ | $30$-$45$ | $45$-$60$ | $60$-$75$ | $75$-$90$ |
|-------|----------|-----------|-----------|-----------|-----------|----------|
| Frequency | $10$ | $7$ | $x$ | $15$ | $10$ | $12$ |

Accepted Answer

Step 1: Modal class is $45$-$60$
Step 2: $55 = 45 + 15 	imes \frac{15 - x}{2(15) - x - 10} = 45 + 15 	imes \frac{15 - x}{20 - x}$
Step 3: $\Rightarrow x = 5$

Question

Solution