1. **Stating the problem:** We have a frequency distribution table for heights in centimeters with intervals and their corresponding frequencies: 120 < x \leq 130 with frequency 2, 130 < x \leq 140 with frequency 12, and 140 < x \leq 150 with frequency 6. 2. **Understanding the data:** This table shows how many students fall into each height range. The goal is often to analyze or visualize this data, such as finding the total number of students or plotting a histogram. 3. **Calculating total frequency:** Add all frequencies to find the total number of students. $$\text{Total frequency} = 2 + 12 + 6 = 20$$ 4. **Finding midpoints of each class interval:** Midpoints help represent each interval as a single value. - For 120 < x \leq 130: midpoint = $\frac{120 + 130}{2} = 125$ - For 130 < x \leq 140: midpoint = $\frac{130 + 140}{2} = 135$ - For 140 < x \leq 150: midpoint = $\frac{140 + 150}{2} = 145$ 5. **Using midpoints and frequencies:** These can be used to calculate measures like mean height or to plot a histogram. 6. **Summary:** The frequency distribution is clear, with most students (12) in the 130-140 cm range, fewer in the other ranges. Final answer: Total students = 20, midpoints = 125, 135, 145 for the intervals respectively.