1. **Stating the problem:** We are given a frequency distribution of mass (in mg) intervals and their corresponding absolute frequencies (AF). The problem is to analyze or interpret this data. 2. **Understanding the data:** The intervals represent ranges of mass values, and AF represents how many observations fall into each interval. 3. **Calculating the total number of observations:** Sum all AF values: $$32 + 57 + 96 + 131 + 158 + 160 + 143 + 103 + 62 + 40 = 982$$ 4. **Calculating the midpoint of each interval:** The midpoint $m_i$ of an interval $[a,b[$ is given by: $$m_i = \frac{a + b}{2}$$ For example, for $[214,217[$: $$m_1 = \frac{214 + 217}{2} = 215.5$$ 5. **Calculating the mean mass:** The mean $\bar{x}$ is calculated by: $$\bar{x} = \frac{\sum (m_i \times AF_i)}{\sum AF_i}$$ Calculate each $m_i \times AF_i$ and sum: $$215.5 \times 32 + 218.5 \times 57 + 221.5 \times 96 + 224.5 \times 131 + 227.5 \times 158 + 230.5 \times 160 + 233.5 \times 143 + 236.5 \times 103 + 239.5 \times 62 + 242.5 \times 40$$ 6. **Performing the calculations:** $$\begin{aligned} &215.5 \times 32 = 6896 \\ &218.5 \times 57 = 12454.5 \\ &221.5 \times 96 = 21264 \\ &224.5 \times 131 = 29419.5 \\ &227.5 \times 158 = 35945 \\ &230.5 \times 160 = 36880 \\ &233.5 \times 143 = 33390.5 \\ &236.5 \times 103 = 24339.5 \\ &239.5 \times 62 = 14849 \\ &242.5 \times 40 = 9700 \\ \end{aligned}$$ Sum these: $$\sum (m_i \times AF_i) = 6896 + 12454.5 + 21264 + 29419.5 + 35945 + 36880 + 33390.5 + 24339.5 + 14849 + 9700 = 224138$$ 7. **Calculate the mean:** $$\bar{x} = \frac{224138}{982} \approx 228.2$$ **Final answer:** The mean mass of the sample is approximately $228.2$ mg.