1. We are given the frequency table for length intervals and need to find the missing cumulative frequency table values $A$, $B$, and $C$. 2. Cumulative frequency is the running total of frequencies up to the upper boundary of the interval. 3. From the first table, the frequencies for intervals are: - $4 < x \leq 8$: 4 - $8 < x \leq 12$: 15 - $12 < x \leq 16$: 7 - $16 < x \leq 20$: 4 4. The cumulative frequencies are calculated by adding frequencies up to that point: - For $4 < x \leq 8$: cumulative frequency is 4 (given) - For $4 < x \leq 12$: cumulative frequency is $4 + 15 = 19$ (given) 5. For the interval $A < x \leq B$: cumulative frequency $C$ corresponds to the next cumulative frequency after $4 < x \leq 12$, which covers the interval $12 < x \leq 16$. 6. Calculate cumulative frequency for $12 < x \leq 16$ (which gives $C$): $$ C = 19 + 7 = 26 $$ 7. The lower limit $A$ of this interval is 12, the upper limit $B$ is 16. 8. Finally, verify cumulative frequency for $4 < x \leq 20$: $$ 4 + 15 + 7 + 4 = 30 $$ Which matches the given total. **Answer:** - $A = 12$ - $B = 16$ - $C = 26$