To determine how the median of the set changes with the addition of the number 87, we first need to find the current median of the existing numbers.
The set of numbers is: 774836924771388377
Since there is only one number in this set, the median is the number itself:
Current median = 774836924771388377
Now, let's add the number 87 to the set:
- New set: {774836924771388377, 87}
Next, we need to arrange the numbers in ascending order:
- The ordered set is: {87, 774836924771388377}
Now, since there are 2 numbers in the new set, the median will be the average of the two middle numbers. So:
New median = (87 + 774836924771388377) / 2
Since 774836924771388377 is much larger than 87, the new median will still be closer to 774836924771388377.
To summarize:
- Current median = 774836924771388377
- New median after adding 87 ≈ 387418462385694185 (but mathematically the median would still lean toward the original high value).
Comparing the two medians:
- Since the new number 87 is significantly smaller than the original number, the median does decrease.
Therefore, the median of the set decreases when 87 is added.