{31;62;-47;20;-54;689;-112;407;-307}

To prepare for your university exams, you can start by organizing and analyzing the given set of numbers: 31, 62, -47, 20, -54, 689, -112, 407, -307.

1. Arrange the numbers in ascending order: -307, -112, -54, -47, 20, 31, 62, 407, 689

2. Find the mean (average) of the numbers: Mean = (Sum of all numbers) / (Total number of numbers)

Sum of the numbers = -307 - 112 - 54 - 47 + 20 + 31 + 62 + 407 + 689 = 689 Total number of numbers = 9

Mean = 689 / 9 = 76.6

3. Find the median of the numbers: The median is the middle number when the numbers are arranged in ascending order. If there are an odd number of numbers, the median is the middle number. If there are an even number of numbers, the median is the average of the two middle numbers.

Since there are 9 numbers, the middle number will be the median.

Median = 31

4. Find the mode of the numbers (if it exists): The mode is the number that appears most frequently in the set of numbers. In this case, there is no number that appears more than once, so there is no mode.

5. Find the range of the numbers: The range is the difference between the largest and smallest numbers in the set.

Largest number = 689 Smallest number = -307

Range = Largest number - Smallest number = 689 - (-307) = 996

By organizing and analyzing the given set of numbers, we have calculated the mean (average) to be 76.6, the median to be 31, the mode to be None, and the range to be 996. These calculations can help provide a better understanding and context for the given numbers in preparation for your university exams.