1. The problem asks which data set could NOT be represented by the given histogram. 2. The histogram shows three intervals with frequencies: - Interval 0-4: frequency 3 - Interval 5-9: frequency 5 - Interval 10-14: frequency 2 3. This means any data set represented by this histogram must have exactly 3 data points between 0 and 4, 5 data points between 5 and 9, and 2 data points between 10 and 14. 4. To check if a data set could be represented, count how many data points fall into each interval and compare with the histogram frequencies. 5. If any interval's count does not match the histogram frequency, that data set could NOT be represented by this histogram. 6. For example, if a data set has 4 points in 0-4, it cannot be represented because the histogram shows only 3. 7. Therefore, the key rule is: the frequency of data points in each interval must exactly match the histogram bar heights. Final answer: Any data set whose counts per interval differ from (3, 5, 2) for intervals (0-4, 5-9, 10-14) respectively could NOT be represented by this histogram.