1. The problem asks which data set could NOT be represented by the given histogram. 2. The histogram shows three intervals on the x-axis: 0-4, 5-9, and 10-14. 3. The heights of the bars represent frequencies: 3 for 0-4, 5 for 5-9, and 2 for 10-14. 4. This means the data set must have exactly 3 values between 0 and 4 inclusive, 5 values between 5 and 9 inclusive, and 2 values between 10 and 14 inclusive. 5. Any data set that does not have these exact counts in these intervals cannot be represented by this histogram. 6. For example, a data set with 4 values in 0-4 or 6 values in 5-9 would not match the histogram. 7. Therefore, to check if a data set could be represented, count how many data points fall into each interval and compare to the histogram frequencies. 8. If the counts match 3, 5, and 2 respectively, the data set could be represented; otherwise, it could not.