Here are the steps you could follow.
1. Sort the points based on "Shape" attribute. You may skip this step if your points are already sorted spatially.
2. Convert Points to Line. Don't worry about the attributes. You will get them in the subsequent steps.
3. Next, we will generate points along the line at 100 km distance. You may use Generate Points Along Lines (Data Management) . Fill the parameters, as required. Keep "Include End Points" option unchecked.
4. Now, using the the above points, we will divide the line, using Split Line at Point (Data Management) . You may choose a Search Radius of 500 meters (just to be safe).
5. Now let's join the attributes of the original points layer to the Split Line layer. You will choose Spatial Join (Analysis) for this.
Target Features: Split Line Layer
Join Features: Original Point Layer
Join Type: One_to_One
Field Map: Delete the fields you don't want to join. For each of the percentile fields, click the field-name > Select "Median" for Merge Rule. Do it for all the required fields. Run the tool.
Hope you will receive the desired result.
Think Location