1. **State the problem:** We have a dot plot showing the number of candy pieces in individual packs. We need to determine which statement about the data is NOT true. 2. **List the data points from the dot plot:** - 10 pieces: 3 packs - 11 pieces: 3 packs - 12 pieces: 0 packs - 13 pieces: 2 packs - 14 pieces: 3 packs - 15 pieces: 3 packs - 16 pieces: 2 packs - 17 pieces: 0 packs - 18 pieces: 3 packs - 19 pieces: 0 packs 3. **Calculate the total number of data points:** $$3 + 3 + 0 + 2 + 3 + 3 + 2 + 0 + 3 + 0 = 19$$ 4. **Find the median:** - The median is the middle value when data is ordered. - Since there are 19 data points, the median is the 10th value. - List data in order: - 10 (3 times): positions 1-3 - 11 (3 times): positions 4-6 - 13 (2 times): positions 7-8 - 14 (3 times): positions 9-11 - The 10th value is in the 14s. - So, median = 14 pieces. 5. **Check statement A:** "The median is 15 pieces of candy." - Our calculation shows median = 14, so statement A is false. 6. **Calculate the range:** - Range = max value - min value - Max value with dots = 18 - Min value with dots = 10 - Range = 18 - 10 = 8 pieces - Statement B says range is 8 pieces, which is true. 7. **Calculate the interquartile range (IQR):** - Q1 is the 25th percentile, position = $\frac{19+1}{4} = 5$th value. - Q3 is the 75th percentile, position = $3 \times \frac{19+1}{4} = 15$th value. - Find Q1 (5th value): - Positions 1-3: 10 - Positions 4-6: 11 - 5th value is 11 - Find Q3 (15th value): - Positions 9-11: 14 - Positions 12-14: 15 - Positions 15-16: 16 - 15th value is 15 - IQR = Q3 - Q1 = 15 - 11 = 4 pieces - Statement C says IQR is 5 pieces, which is false. 8. **Calculate the mean:** - Multiply each value by its frequency and sum: $$10 \times 3 + 11 \times 3 + 13 \times 2 + 14 \times 3 + 15 \times 3 + 16 \times 2 + 18 \times 3 = 30 + 33 + 26 + 42 + 45 + 32 + 54 = 262$$ - Mean = $\frac{262}{19} \approx 13.79$ - Statement D says mean is 15, which is false. 9. **Conclusion:** - Statements A, C, and D are false. - Statement B is true. - The question asks which statement is NOT represented by the data. - The first false statement is A. **Final answer:** Statement A is not represented by the data.