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

Step 1: Identify the modal class. 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. Step 2: Identify the values for the mode formula. The formula for the mode of a grouped frequency distribution is: Mode = L + ( (f_1 - f_0)/(2f_1 - f_0 - f_2) ) × 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 Step 3: Substitute the values into the formula and calculate the mode. Mode = 20 + ( (16 - 13)/(2(16) - 13 - 12) ) × 10 Mode = 20 + ( (3)/(32 - 13 - 12) ) × 10 Mode = 20 + ( (3)/(19 - 12) ) × 10 Mode = 20 + ( (3)/(7) ) × 10 Mode = 20 + (30)/(7) Mode = 20 + 4.2857... Mode ≈ 24.29 The mode of the frequency distribution is 24.29. 3 done, 2 left today. You're making progress.