Final answer:
The median of the ordered data set 3.1, 3.1, 3.6, 3.6, 3.8, 4, 4.2, 4.5, 4.8, 4.9 is 3.9, calculated by averaging the 5th and 6th terms. The range is 1.8, found by subtracting the smallest value from the largest.
Step-by-step explanation:
To find the median of the given data set 3.1, 3.1, 3.6, 3.6, 3.8, 4, 4.2, 4.5, 4.8, 4.9, we first need to make sure that the data is ordered from least to greatest, which it already is. Since there are an even number of data values (10 in this case), the median will be the average of the two middle values. The two middle values are the 5th and 6th terms, which are 3.8 and 4. To find the median, we add the two numbers together and divide by two: (3.8 + 4) / 2 = 3.9. Therefore, the median is 3.9.
To find the range of the data, we subtract the smallest value in the set from the largest value. The smallest value is 3.1 and the largest is 4.9. Thus, the range is 4.9 - 3.1 = 1.8.