Short Answer 
The weights should first be organized in ascending order before calculating the mean, median, and mode. The mean weight is 80kg, the median is 76kg, and the mode is 61kg.
Step 1: Order the Numbers
Begin by organizing the weights into ascending order to facilitate easier calculations. List the weights clearly in sequence:
- 53kg
- 55kg
- 61kg
- 61kg
- 76kg
- 91kg
- 98kg
- 105kg
- 120kg
Step 2: Calculate the Mean
To find the mean, sum all the weights together and then divide by the total number of weights. In this case, add: 53 + 55 + 61 + 61 + 76 + 91 + 98 + 105 + 120 to get a total of 720, and then divide by 9, which gives:
- Mean = 720 / 9 = 80
Step 3: Determine the Median and Mode
The median is the middle value of your ordered list. With 9 numbers, the median is the 5th number, which is 76kg. For the mode, identify the value that appears most frequently in the list; here, 61kg appears twice, making it the mode. Thus:
- Median = 76kg
- Mode = 61kg