Final answer:
The median age from Amelia's survey is the age that appears in the 10th and 11th positions of the ordered list, which are both 14. Hence, the median age is 14 years.
Step-by-step explanation:
To find the median age from Amelia's survey results, we first need to list out all the ages in ascending order based on their frequency. However, instead of listing each age out individually, we can determine the position of the median age in the list using the formula: Median position = (Total number of observations + 1) / 2.
The total number of observations (sum of frequencies) is 3+4+2+4+5+2 = 20. Thus, the median position will be (20+1)/2 = 10.5, which means that the median is the average of the 10th and 11th values in the ordered list.
Before finding these values, we need to order the ages by frequency:
- 11-year-olds: 3 times
- 12-year-olds: 4 times
- 13-year-olds: 2 times
- 14-year-olds: 4 times
- 15-year-olds: 5 times
- 16-year-olds: 2 times
So, the ordered list of ages will be: 11, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16. The 10th and 11th values are both 14. Therefore, the median age is 14.