Find the mode of the following frequency distribution: Variable 10 20 30 40 50 Frequency 4 13 16 12 5

The modal class is the class with the highest frequency.
From the given data:

Variable	Frequency
0-10	4
10-20	13
20-30	16
30-40	12
40-50	5

The highest frequency is 16, which corresponds to the class interval 20-30.
So, the modal class is 20-30.

The formula for the mode of a grouped frequency distribution is:

$$\text{Mode} = L + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h$$

Where:

• $L$ = Lower limit of the modal class = 20
• $f_1$ = Frequency of the modal class = 16
• $f_0$ = Frequency of the class preceding the modal class = 13
• $f_2$ = Frequency of the class succeeding the modal class = 12
• $h$ = Class size (upper limit - lower limit) = $30 - 20 = 10$

$$\text{Mode} = 20 + \left( \frac{16 - 13}{2(16) - 13 - 12} \right) \times 10$$ $$\text{Mode} = 20 + \left( \frac{3}{32 - 13 - 12} \right) \times 10$$ $$\text{Mode} = 20 + \left( \frac{3}{19 - 12} \right) \times 10$$ $$\text{Mode} = 20 + \left( \frac{3}{7} \right) \times 10$$ $$\text{Mode} = 20 + \frac{30}{7}$$ $$\text{Mode} = 20 + 4.2857...$$ $$\text{Mode} \approx 24.29$$

The mode of the frequency distribution is 24.29.