When Joe added 20% more data points to the dataset, the data points in the dataset increased by 20/100*200 = <<20/100*200=40>>40 data points.
The total number of data points increased to 200+40 = <<200+40=240>>240
If he reduced the data points by 1/4 of the total data points, the data points reduced by 1/4*240 =60
The total number of data points left in the dataset after Joe reduced the data points by 1/4 of the total data points is 240-60= <<240-60=180>>180
#### 180