1. **State the problem:** We need to complete the five number summary (Minimum, Lower quartile, Median, Upper quartile, Maximum) for the data set: 25, 26, 27, 28, 29, 30 with the given frequencies. 2. **List the data with frequencies:** - 25 appears 4 times - 26 appears 1 time - 27 appears 4 times - 28 appears 3 times - 29 appears 2 times - 30 appears 3 times 3. **Create the ordered data set:** $$\underbrace{25, 25, 25, 25}_{4}, 26, \underbrace{27, 27, 27, 27}_{4}, \underbrace{28, 28, 28}_{3}, \underbrace{29, 29}_{2}, \underbrace{30, 30, 30}_{3}$$ 4. **Count total data points:** $$4 + 1 + 4 + 3 + 2 + 3 = 17$$ 5. **Find the Median:** Median is the middle value, position $$\frac{17 + 1}{2} = 9$$th data point. Counting the data points: - First 4 are 25 - 5th is 26 - 6th to 9th are 27 So, the 9th data point is 27. 6. **Find the Lower Quartile (Q1):** Q1 is the median of the lower half (first 8 data points). The first 8 data points are: 25, 25, 25, 25, 26, 27, 27, 27 Median position for Q1 is $$\frac{8 + 1}{2} = 4.5$$, average of 4th and 5th data points. 4th data point = 25, 5th data point = 26 So, $$Q1 = \frac{25 + 26}{2} = 25.5$$ 7. **Find the Upper Quartile (Q3):** Q3 is the median of the upper half (last 8 data points). The last 8 data points are: 27, 28, 28, 28, 29, 29, 30, 30 Median position for Q3 is $$4.5$$, average of 4th and 5th data points. 4th data point = 28, 5th data point = 29 So, $$Q3 = \frac{28 + 29}{2} = 28.5$$ 8. **Maximum:** Given as 30. **Final five number summary:** - Minimum: 25 - Lower quartile (Q1): 25.5 - Median: 27 - Upper quartile (Q3): 28.5 - Maximum: 30