This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To calculate the cumulative frequency (cf) for a frequency distribution table, you add the frequency of each class to the cumulative frequency of the previous class. Here's how to calculate the 'cf' column based on the 'Freq' column you provided: Step 1: For the first class, the cumulative frequency is equal to its frequency. For the age group 10-19: cf = Freq = 6 Step 2: For the second class, add its frequency to the cumulative frequency of the previous class. For the age group 20-29: cf = (cf of 10-19) + (Freq of 20-29) = 6 + 12 = 18 Step 3: Continue this process for each subsequent class. For the age group 30-39: cf = (cf of 20-29) + (Freq of 30-39) = 18 + 16 = 34 (Note: Your table shows 33 here, but based on the frequencies, it should be 34.) For the age group 40-49: cf = (cf of 30-39) + (Freq of 40-49) = 34 + 9 = 43 (Note: Your table shows 42 here, which would be correct if the previous cf was 33, but based on the correct calculation, it should be 43.) For the age group 50-59: cf = (cf of 40-49) + (Freq of 50-59) = 43 + 2 = 45 (Note: Your table shows 47 here, which is inconsistent with the frequencies.) For the age group 60-69: cf = (cf of 50-59) + (Freq of 60-69) = 45 + 2 = 47 (Note: Your table shows 49 here, which is inconsistent. The final cumulative frequency should equal the total sum of frequencies, which is 6+12+16+9+2+2 = 47. Your table shows a total frequency of 50, which also doesn't match the sum of the individual frequencies.) Here is the corrected 'cf' column: • 10-19: cf = 6 • 20-29: cf = 18 • 30-39: cf = 34 • 40-49: cf = 43 • 50-59: cf = 45 • 60-69: cf = 47 The correctly calculated cumulative frequencies are: c 6 \\ 18 \\ 34 \\ 43 \\ 45 \\ 47 3 done, 2 left today. You're making progress.