1. **Problem Statement:** Calculate the Five-Number Summary for Kusal Mendis's match scores: 35, 42, 50, 48, 55, 45, 53, 51, 38, 60, 40, 57, 5, 47, 49. 2. **Five-Number Summary Definition:** The Five-Number Summary consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum of the dataset. 3. **Step 1: Sort the data:** $$5, 35, 38, 40, 42, 45, 47, 48, 49, 50, 51, 53, 55, 57, 60$$ 4. **Step 2: Find the minimum and maximum:** - Minimum = 5 - Maximum = 60 5. **Step 3: Find the median (Q2):** - Number of data points $n=15$ (odd) - Median is the middle value at position $\frac{n+1}{2} = 8$th value - Median = 48 6. **Step 4: Find Q1 (median of lower half):** - Lower half (first 7 values): $5, 35, 38, 40, 42, 45, 47$ - Median of lower half is 4th value = 40 7. **Step 5: Find Q3 (median of upper half):** - Upper half (last 7 values): $49, 50, 51, 53, 55, 57, 60$ - Median of upper half is 4th value = 53 8. **Five-Number Summary:** - Minimum = 5 - Q1 = 40 - Median = 48 - Q3 = 53 - Maximum = 60 9. **Boxplot:** The boxplot visually represents these five numbers with a box from Q1 to Q3, a line at the median, and whiskers extending to the minimum and maximum. 10. **Interpretation:** - The data is slightly right-skewed due to the minimum being much lower (5) than Q1. - Most scores lie between 40 and 53. - The median score is 48, indicating half the scores are below and half above. 11. **Suitable Measure of Central Tendency:** - Median is preferred here because the data has an outlier (5) which can skew the mean. - Median is robust to outliers and better represents the central location. 12. **Performance Bonus Calculation:** - Current total score for 15 matches: $5 + 35 + 38 + 40 + 42 + 45 + 47 + 48 + 49 + 50 + 51 + 53 + 55 + 57 + 60 = 765$ - Required average for 16 matches $> 55$ - Total required score $> 55 \times 16 = 880$ - Minimum score needed in next match $= 880 - 765 = 115$ **Final answers:** - Five-Number Summary: Minimum = 5, Q1 = 40, Median = 48, Q3 = 53, Maximum = 60 - Minimum next match score to exceed average 55 = 115