Find the mode of the following distribution:

| Marks | $0$-$10$ | $10$-$20$ | $20$-$30$ | $30$-$40$ | $40$-$50$ | $50$-$60$ |
|-------|----------|-----------|-----------|-----------|-----------|-----

Question

Find the mode of the following distribution:

| Marks | $0$-$10$ | $10$-$20$ | $20$-$30$ | $30$-$40$ | $40$-$50$ | $50$-$60$ |
|-------|----------|-----------|-----------|-----------|-----------|----------|
| Number of Students | $4$ | $6$ | $7$ | $12$ | $5$ | $6$ |

Accepted Answer

Step 1: Modal class: $30$-$40$ (highest frequency $= 12$). Here $l = 30$, $f_1 = 12$, $f_0 = 7$, $f_2 = 5$, $h = 10$.
Step 2: Mode $= l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} 	imes h = 30 + \frac{12 - 7}{2(12) - 7 - 5} 	imes 10$
Step 3: $= 30 + \frac{5}{12} 	imes 10 = 30 + 4.17 = 34.17$

Question

Solution