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I have data that locates places by xy coordinate.

I have plotted them on a shapefile.

As you can from the sample map I have uploaded, many of the xy coordinates are incorrect and locate places outside of the shapefile, and therefore need to be removed from my dataset.

Some of the incorrect coordinates have a y coordinate = 0 (the vertical line of points), and are easily removed, by dropping observations where y is = 0.

However, there are many other coordinates (not all represented by this map), that are incorrect but are not equal to 0 and therefore not easily identified.

It would be very timely to identify 10 years of measurement errors individually.

So, I was thinking that an easy way to remove these points is to delete the observations situated outside of the shapefile/island.

I am still an ArcGis beginner, so I am not confident yet on how to manipulate the data in such a way.

Do you know if it is possible, and how to go about it?

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Here are some alternatives to Select by Location:

Intersect (Analysis)

Computes a geometric intersection of the input features. Features or portions of features which overlap in all layers and/or feature classes will be written to the output feature class.

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Clip (Analysis)

Extracts input features that overlay the clip features.

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This is a simple selection by location process. My recommendation is to go to your Selection tab -> Select by Location. Select features from your target layer (your points). Your source layer will be your polygon. For your spatial selection method you will choose "are within the source layer feature." Click OK. Your desired data will be selected. Now, just right click on the layer in the TOC and export the data as a new shapefile or feature class.

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    You'd want to switch selection, to select the points that are outside the polygon.
    – Maksim
    Commented Jul 7, 2015 at 15:32
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    If you were deleting them in an editing session. The process I described above is simply creating a new dataset without the unwanted points. Same result, different process
    – Chris Strother
    Commented Jul 7, 2015 at 15:34
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    Particularly for a beginner, I'd go with @Chris_Strother 's method, just so that none of the original data is lost. Another issue might be what the OP means by 'incorrect'. If it implies 'unwanted', then either method will work. If it means 'incorrect coordinates', then the OP has a whole other issue.
    – recurvata
    Commented Jul 7, 2015 at 15:45

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