Final answer:
The mode is the value that appears most frequently in a data set. For the set of numbers 20, 26, 46, 26, 49, 26, 49, the mode is 26. In examples provided, the modes are 72 for the exam scores data and 7 for the library books data.
Step-by-step explanation:
The mode in statistics is the value that appears most frequently in a data set. A data set may have one mode, more than one mode (in which case it's called bimodal or multimodal), or no mode at all if all values appear with the same frequency.
Looking at the set of numbers 20, 26, 46, 26, 49, 26, 49, to determine the mode, we start by counting the frequency of each number:
- 20 appears once
- 26 appears three times
- 46 appears once
- 49 appears twice
Since the number 26 appears the most frequently (three times), 26 is the mode of this data set.
For the example provided with the statistics exam scores, the mode is 72 since it appears five times, which is more than any other number in the list.
Similarly, for the number of books checked out from the library by students, we find that the number 0 appears three times, the number 7 appears four times, and the number 8 appears three times. Therefore, the mode for this data set is 7 as it has the highest frequency.