1. **State the problem:** We are given a stem-and-leaf plot representing club sizes and a frequency table with some missing values. We need to fill in the missing frequencies for the intervals 31-40 and 51-60. 2. **Understand the stem-and-leaf plot:** Each stem represents the tens digit, and each leaf represents the units digit of club sizes. - Stem 2: Leaves 1, 1, 3, 5, 9 correspond to club sizes 21, 21, 23, 25, 29 (5 clubs) - Stem 3: Leaves 1, 6 correspond to 31, 36 (2 clubs) - Stem 4: Leaf 5 corresponds to 45 (1 club) - Stem 5: Leaves 2, 9, 9 correspond to 52, 59, 59 (3 clubs) - Stem 6: Leaves 2, 4, 6, 8 correspond to 62, 64, 66, 68 (4 clubs) - Stem 7: Leaf 1 corresponds to 71 (1 club) - Stem 8: Leaves 3, 3, 7, 9 correspond to 83, 83, 87, 89 (4 clubs) - Stem 9: Leaf 0 corresponds to 90 (1 club) 3. **Use the stem-and-leaf plot to fill the frequency table:** - 21-30: 5 clubs (given) - 31-40: Count from stem 3: 2 clubs (31, 36) - 41-50: 1 club (45) - 51-60: Count from stem 5: 3 clubs (52, 59, 59) - 61-70: 4 clubs (62, 64, 66, 68) - 71-80: 1 club (71) - 81-90: Count from stems 8 and 9: 4 + 1 = 5 clubs (83, 83, 87, 89, 90) 4. **Final frequency table:** | Number of members | Number of clubs | |-------------------|-----------------| | 21-30 | 5 | | 31-40 | 2 | | 41-50 | 1 | | 51-60 | 3 | | 61-70 | 4 | | 71-80 | 1 | | 81-90 | 5 |