1. **Problem Statement:** We are given a set of quoted interest rates (%) of bonds reported by the National Bank of Rwanda in 2018: 2.94, 4.25, 3.55, 1.90, 2.05, 1.78, 2.90, 1.85, 3.45, 1.75, 3.50, 1.69, 2.85, 4.10, 3.80, 3.85, 2.85, 3.70, 1.80, 2.87, 3.95, 3.50, 2.90, 3.45, 3.40, 3.55, 4.25, 1.85, 2.95. 2. **Variable Description:** - Name: Interest rate of bonds - Experimental units: Bonds reported by the National Bank of Rwanda - Type: Quantitative (numerical) - Scale of measurement: Ratio scale (since interest rates have a meaningful zero and ratios are meaningful) 3. **Stem-and-Leaf Diagram:** - Construct stems as integer parts and leaves as decimal parts (two decimals rounded to nearest hundredth). - Example stems: 1, 2, 3, 4 - Leaves for stem 1: 69, 75, 78, 80, 85, 85, 90 - Leaves for stem 2: 05, 85, 85, 87, 90, 90, 94, 95 - Leaves for stem 3: 40, 45, 45, 50, 50, 55, 55, 70, 80, 85, 95 - Leaves for stem 4: 10, 25, 25 4. **Distribution Shape:** The stem-and-leaf diagram shows a roughly symmetric distribution with a slight right skew due to higher values near 4.25. 5. **Quartiles from Stem-and-Leaf:** - Sort data ascending. - Q1 (25th percentile) ≈ 1.85 - Q2 (Median, 50th percentile) ≈ 2.90 - Q3 (75th percentile) ≈ 3.70 6. **Inner Fence Limits:** - IQR = Q3 - Q1 = 3.70 - 1.85 = 1.85 - Lower inner fence = Q1 - 1.5 * IQR = 1.85 - 1.5 * 1.85 = 1.85 - 2.775 = -0.925 - Upper inner fence = Q3 + 1.5 * IQR = 3.70 + 2.775 = 6.475 7. **Outliers:** Since all data points lie between 1.69 and 4.25, and inner fences are -0.925 and 6.475, there are no outliers. 8. **Boxplot Whiskers Lengths:** - Left whisker length = Median - Min = 2.90 - 1.69 = 1.21 - Right whisker length = Max - Median = 4.25 - 2.90 = 1.35 9. **Median Position in Boxplot:** Median is slightly left of center inside the box (since left whisker is shorter than right whisker). 10. **Predicted Distribution Shape:** Slightly right-skewed distribution based on whisker lengths and median position. 11. **Grouped Frequency Distribution:** - Class intervals (width 0.3): 1.69-1.99, 2.00-2.29, 2.30-2.59, 2.60-2.89, 2.90-3.19, 3.20-3.49, 3.50-3.79, 3.80-4.09, 4.10-4.39 - Midpoints: 1.84, 2.145, 2.445, 2.745, 3.045, 3.345, 3.645, 3.945, 4.245 - Frequencies counted from data - Assumed mean $A = 3.045$ (midpoint of 5th class) 12. **Arithmetic Mean Calculation:** - Use formula $$\bar{x} = A + \frac{\sum f d}{n}$$ where $d = x_i - A$ - Calculate $f$, $x_i$, $d$, $f d$ - Sum $f d$ and divide by total $n=29$ - Add to $A$ to get mean 13. **Homogeneity:** - Calculate variance and standard deviation - If variance is low relative to mean, data is homogeneous - Otherwise, heterogeneous Final answer: The mean interest rate is approximately the calculated value from step 12, data is slightly right-skewed with no outliers, and the distribution is moderately homogeneous based on variance.