1. **State the problem:** We have a frequency distribution with class intervals and their frequencies. We want to draw a histogram and find the mode of the distribution. 2. **Recall the mode in grouped data:** The mode is the value that appears most frequently. For grouped data, the mode lies in the class interval with the highest frequency, called the modal class. 3. **Identify the modal class:** From the frequencies given: 3, 5, 10, 12, 7, 3, the highest frequency is 12 corresponding to the class interval $10.4 - 12.6$. 4. **Use the mode formula for grouped data:** $$\text{Mode} = L + \frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)} \times h$$ where: - $L$ = lower boundary of modal class = 10.4 - $f_1$ = frequency of modal class = 12 - $f_0$ = frequency of class before modal class = 10 - $f_2$ = frequency of class after modal class = 7 - $h$ = class width = $12.6 - 10.4 = 2.2$ 5. **Calculate the mode:** $$\text{Mode} = 10.4 + \frac{(12 - 10)}{(2 \times 12 - 10 - 7)} \times 2.2$$ $$= 10.4 + \frac{2}{(24 - 17)} \times 2.2$$ $$= 10.4 + \frac{2}{7} \times 2.2$$ $$= 10.4 + 0.6286$$ $$= 11.0286$$ 6. **Interpretation:** The mode of the distribution is approximately $11.03$, which lies within the modal class $10.4 - 12.6$. 7. **Histogram description:** The histogram bars correspond to the class intervals on the x-axis and frequencies on the y-axis. The tallest bar is for $10.4 - 12.6$ with height 12, confirming the modal class. **Final answer:** The mode of the distribution is approximately $11.03$.