Single data point, over a range of time - distribution?

Question

I have chemistry data of rocks, with assigned age intervals. What I want to do is plot these/analyse these together. My problem is how to deal with this singular data point specified over different time intervals.

e.g.:

Data1: Silica = $76$, age = $2200$ - $2400$ Mya

Data2: Silica = $64$, age = $2100$ - $2300$ Mya

If I want to analyse data between an age range of e.g. $2100$ - $2250$ Mya, how would I go about doing this? Do I assign the value across the entire range, or do I do some kind of normal distribution of the data across the range. I believe the age ranges are confidence limits on whatever age analysis was done (assume $95\%$). If i assign it across the entire interval, it means the Data1 will be 'counted' twice in any analysis e.g. if i choose to look at $2200$ - $2300$ Mya averages/analysis, and then $2300$ - $2400$ Mya. If i treat it as a distribution though, the value i plot will be lower than the measured value - but is this the correct way to deal with it?

A diagram to maybe help explain what I mean: Overlapping time ranges, with a single value for each range. Do I apply a weight/distribution to the value over the range like below, or do i apply the measured value across the entire range.

  Silica↑     _
            _   _
          _       _
        |-----------|
      2400         2200
                    _
                  _   _
                _       _
              |------------|
             2300         2100
  Time→