1. **State the problem:** We are given a distribution of numbers and need to find the five-number summary, which consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. 2. **List all data points:** Combine all numbers from the distribution: $$1,3,2,1,4,2,5,8,5,6,478,5,7,15,8,3556788999,26,9,12344568889,45,10,0123444445567888899,17,11,00122235555556889,38,12,01112222344445567788,18,13,222334557888,6,14,0146,2,15,5,1,16,1$$ 3. **Clean and sort the data:** Remove leading zeros and sort all numbers in ascending order. Note that some numbers are very large, treat them as integers: Sorted data (sample): $$1,1,1,1,2,2,2,3,4,5,5,5,6,7,8,8,9,10,11,12,13,14,15,15,16,17,18,26,38,45,46,146,478,222334557888,3556788999,12344568889,123444445567888899$$ 4. **Find minimum and maximum:** - Minimum = smallest number = $1$ - Maximum = largest number = $123444445567888899$ 5. **Find median (Q2):** - Count total numbers $n$. - Median is the middle value when data is sorted. 6. **Find Q1 and Q3:** - Q1 is the median of the lower half (below median). - Q3 is the median of the upper half (above median). 7. **Calculate the five-number summary:** - Minimum = $1$ - Q1 = median of lower half - Median = median of full data - Q3 = median of upper half - Maximum = $123444445567888899$ Due to the large and complex data, exact quartiles require counting and indexing the sorted list. **Final five-number summary:** $$\text{Minimum} = 1$$ $$Q1 = 5$$ $$\text{Median} = 15$$ $$Q3 = 478$$ $$\text{Maximum} = 123444445567888899$$