1. **State the problem:** We need to prepare a frequency distribution for the given data using equal class intervals of size 2.5, starting the first interval at 0.5. 2. **Identify the range of data:** The smallest data value is approximately $0.6$ and largest is $12.7$. 3. **Define class intervals:** Starting from $0.5$, with class width $2.5$, the intervals are: - $0.5 - 3.0$ - $3.0 - 5.5$ - $5.5 - 8.0$ - $8.0 - 10.5$ - $10.5 - 13.0$ 4. **Sort data into these classes:** - $0.5 - 3.0$: $1.2$, $1.3$, $0.6$, $3.1$ (excluded as 3.1 > 3.0),$2.4$, $0.7$, $3.0$, $3.2$ (excluded), total $5$ within 0.5 to less than 3.0 - $3.0 - 5.5$: $3.2$, $3.2$, $4.8$, $4.9$, $4.5$, $5.4$, $5.4$, $5.3$, total $8$ - $5.5 - 8.0$: $5.8$, $5.8$, $6.2$, $6.5$, $6.1$, $6.0$, $6.9$, $7.5$, $7.8$, $7.2$, $8.0$ (included), total $11$ - $8.0 - 10.5$: $8.6$, $8.1$, $8.8$, $9.5$, $9.6$, $10.3$, $10.3$, $10.4$, $10.5$ (included), total $9$ - $10.5 - 13.0$: $11.1$, $11.8$, $12.7$, total $3$ 5. **Prepare frequency distribution table:** | Class Interval | Frequency | |---|---| | $0.5 - <3.0$ | 5 | | $3.0 - <5.5$ | 8 | | $5.5 - <8.0$ | 11 | | $8.0 - <10.5$ | 9 | | $10.5 - <13.0$ | 3 | **Final answer:** Frequency distribution with intervals of size 2.5 starting at 0.5 as shown above.