How do you calculate cumulative frequency from a frequency distribution table?

For the age group 10-19:

$$\text{cf} = \text{Freq} = 6$$

For the age group 20-29:

$$\text{cf} = (\text{cf of 10-19}) + (\text{Freq of 20-29}) = 6 + 12 = 18$$

For the age group 30-39:

$$\text{cf} = (\text{cf of 20-29}) + (\text{Freq of 30-39}) = 18 + 16 = 34$$

(Note: Your table shows 33 here, but based on the frequencies, it should be 34.)

For the age group 40-49:

$$\text{cf} = (\text{cf of 30-39}) + (\text{Freq of 40-49}) = 34 + 9 = 43$$

(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:

$$\text{cf} = (\text{cf of 40-49}) + (\text{Freq of 50-59}) = 43 + 2 = 45$$

(Note: Your table shows 47 here, which is inconsistent with the frequencies.)

For the age group 60-69:

$$\text{cf} = (\text{cf of 50-59}) + (\text{Freq of 60-69}) = 45 + 2 = 47$$

(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: $\text{cf} = 6$
• 20-29: $\text{cf} = 18$
• 30-39: $\text{cf} = 34$
• 40-49: $\text{cf} = 43$
• 50-59: $\text{cf} = 45$
• 60-69: $\text{cf} = 47$

The correctly calculated cumulative frequencies are:

$$\begin{array}{c} 6 \\ 18 \\ 34 \\ 43 \\ 45 \\ 47 \end{array}$$