1. **Stating the problem:** We have a histogram and a partial frequency table showing heights of Year 11 students in Mathstown High School. The height classes are given, and some frequencies and frequency densities are missing. 2. **Understanding the data:** The classes are: - 140 ≤ h < 150 - 150 ≤ h < 160 - 160 ≤ h < 165 - 165 ≤ h < 170 - 170 ≤ h < 180 - 180 ≤ h < 190 - 190 ≤ h < 210 Given frequencies for some classes are 15, 20, and 12, but not all. 3. **Formula for frequency density:** $$\text{Frequency density} = \frac{\text{Frequency}}{\text{Class width}}$$ 4. **Step to complete the table:** - Calculate class widths: - 140–150: width = 10 - 150–160: width = 10 - 160–165: width = 5 - 165–170: width = 5 - 170–180: width = 10 - 180–190: width = 10 - 190–210: width = 20 - Use the histogram bars (frequency densities) to find missing frequencies: For example, if frequency density is known for a class, frequency = frequency density × class width. 5. **Example calculation:** Suppose frequency density for 160 ≤ h < 165 is given as $d$, then frequency = $d \times 5$. 6. **Complete the table:** - Use given frequencies and frequency densities from the histogram to fill missing values. 7. **Complete the histogram:** - Use the completed table frequencies and class widths to calculate frequency densities for missing bars. 8. **Summary:** - Use the formula $\text{Frequency density} = \frac{\text{Frequency}}{\text{Class width}}$ to find missing values. - Fill in the table and histogram accordingly. Since the exact frequency densities or histogram bar heights are not provided in the prompt, the exact numerical completion cannot be done here. **Final answer:** Use the formula and class widths to calculate missing frequencies and frequency densities to complete the table and histogram.