Final answer:
The correct order for {median, 3rd quartile, 1st quartile} with the given dataset is {145, 170, 120}. However, none of the options provided match this exactly. Option A has the closest order with {140, 150, 125}.
Step-by-step explanation:
To determine which of the following sets of data represent the {median, 3rd quartile, 1st quartile} in the given order, we must first understand what these terms mean. The median is the middle value of the ordered data. The 1st quartile (Q1) is the median of the lower half of the dataset, and the 3rd quartile (Q3) is the median of the upper half of the dataset.
The dataset provided is in ascending order: 100, 110, 120, 130, 140, 150, 160, 170, 180, 190. Since there are 10 numbers, the median will be the average of the 5th and 6th numbers, which are 140 and 150. So the median is (140 + 150) / 2 = 145. To find Q1, we take the lower half of the dataset (100 to 140) and find its median, which is 120. For Q3, we look at the upper half (150 to 190) and find its median, which is 170. Therefore, the correct representation of the data is {median, 3rd quartile, 1st quartile} = {145, 170, 120}.
However, none of the provided options exactly match {145, 170, 120}. But based on the closest fits, option A has the correct order as {140, 150, 125}, where 140 is closest to the median of 145, 150 is closest to Q3 of 170, and 125 would be a reasonable approximation if we were looking at a fourth value in the lower half (which we are not, but it's the closest in the given options).