Ireland you say??? Well according to your longitude and latitude fields, they have been swapped.
The coordinate values in those fields are indeed decimal degrees... just in the wrong order.
I would try to add that table as an event layer into ArcMap... in a brand new project with nothing else in it
Make XY Event Layer—Help | ArcGIS for Desktop
just remember your latitude field is actually longitude and longitude is actually latitude.
add it to a geodatabase or make a shapefile or whatever
The output point feature layer created by this tool is temporary and will not persist after the session ends. You can export this event layer to a feature class on disk using the Copy Features, Feature to Point, or Feature Class to Feature Class tool.
I would define it as a GCS WGS84 (aka geographic coordinate system wgs84 datum... aka decimal degree data ... unprojected data) as a good guess. (see below)
Then and only then, add some other data to see if it appears in Ireland and not near the equator
PS you use the Define Projection tool to tell the file what it is Define Projection—Help | ArcGIS for Desktop a GCS WGS 84
if you want some other coordinate system, then you use the Project—Help | ArcGIS for Desktop
