Find the **mode** for the given frequency distribution (rounded off to two decimal places):

| Class Interval | Frequency |
|----------------|-----------|
| 5 – 10 | 8 |
| 10 – 15 | 7 |
| 15 – 20 | 6 |
| 20 – 25 | 9 |
| 25 – 30 | 11 |
| 30 – 35 | 10 |

Question

Find the **mode** for the given frequency distribution (rounded off to two decimal places):

| Class Interval | Frequency |
|----------------|-----------|
| 5 – 10         | 8         |
| 10 – 15        | 7         |
| 15 – 20        | 6         |
| 20 – 25        | 9         |
| 25 – 30        | 11        |
| 30 – 35        | 10        |

Accepted Answer

**Solution:**

1. Identify the modal class: The class interval with the highest frequency is 25 – 30 with frequency $f_m = 11$.

2. Define the variables for the mode formula:
   - Lower limit of modal class, $L = 25$
   - Frequency of modal class, $f_m = 11$
   - Frequency of class preceding modal class, $f_1 = 9$ (for 20 – 25)
   - Frequency of class succeeding modal class, $f_2 = 10$ (for 30 – 35)
   - Class width, $h = 30 - 25 = 5$

3. Use the mode formula for grouped data:
   $$	ext{Mode} = L + \left( \frac{f_m - f_1}{2f_m - f_1 - f_2} ight) 	imes h$$

4. Substitute the values:
   $$	ext{Mode} = 25 + \left( \frac{11 - 9}{2 	imes 11 - 9 - 10} ight) 	imes 5 = 25 + \left( \frac{2}{22 - 9 - 10} ight) 	imes 5 = 25 + \left( \frac{2}{3} ight) 	imes 5$$

5. Calculate:
   $$25 + \frac{10}{3} = 25 + 3.333... = 28.333...$$

6. Round to two decimal places:
   $$28.33$$

**Answer:** The mode of the distribution is **28.33**.

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