1. The problem asks which data set could NOT be represented by the given histogram. 2. The histogram has three bars with frequencies: - 0-4: frequency 3 - 5-9: frequency 5 - 10-14: frequency 2 3. We check each data set to see if their values fit these frequencies. 4. For data set A: {8, 3, 5, 7, 12, 7, 1, 3, 5, 12} - Count values in 0-4: 3, 1, 3 → 3 values - Count values in 5-9: 8, 5, 7, 7, 5 → 5 values - Count values in 10-14: 12, 12 → 2 values This matches the histogram frequencies exactly. 5. For data set B: {9, 3, 5, 13, 11, 7, 1, 3, 5, 9} - Count values in 0-4: 3, 1, 3 → 3 values - Count values in 5-9: 9, 5, 7, 5, 9 → 5 values - Count values in 10-14: 13, 11 → 2 values This also matches the histogram frequencies exactly. 6. Both data sets A and B match the histogram frequencies, so neither is impossible. 7. However, the question asks which data set could NOT be represented by the histogram shown. 8. Since both fit, the answer is neither A nor B could NOT be represented. 9. But since the question expects one answer, we re-examine carefully. 10. Notice in data set B, the value 9 appears twice, which is within 5-9 range, so frequency 5 is correct. 11. Therefore, both data sets can be represented by the histogram. 12. The question likely expects the answer that neither data set contradicts the histogram. Final answer: Neither data set A nor B could NOT be represented by the histogram shown.