Final answer:
The median of gold medal wins may change when the Unified Team's medals are counted towards the Soviet Union's total or considered separately. We cannot determine the exact value of M - N without specific data on gold medals won. Option c) -1 and d) 2 can be dismissed, but between options a) 0 and b) 1, we cannot conclusively decide without more data.
Step-by-step explanation:
The question is about calculating the difference in the median number of gold medals won by countries in two scenarios: with the Unified Team's gold medals counted as the Soviet Union's, and without. When the Unified Team's medals are counted towards the Soviet Union's total, we have 6 countries with a certain number of gold medals each; without those medals, we have 7 countries. We need to find the two medians and their difference.
To find the median in each scenario, we would list the number of gold medals won in ascending order. The median is the middle number in the list if there is an odd number of values, or the average of the two middle numbers if there is an even number of values. With 6 countries, we take the average of the 3rd and 4th values. With 7 countries, the median is the 4th value alone.
Without knowing the exact numbers of gold medals won, we cannot directly calculate the medians. However, given that we are adding in an extra country with possibly a small number of gold medals (the Unified Team), the median of 7 values would likely be lower or the same as the median of 6 values. Thus, the value of M - N is either 0 or a positive number, meaning the options c) -1 and d) 2 are unlikely. Without further information, we cannot determine if M - N is 0 or a positive number (a or b).