Since labeling is part of the base layer properties, you cannot label the objects individually. Either all the objects in the base layer are labeled with the selected attribute, or all of them are not.
However, if you just want to label some of the objects with a particular attribute, you can create a new attribute for that object and set the label source to be that attribute.
- Select the Base layer in the Contents window and click Map Tools | Layer Tools | Open Attribute Table.
- In the Attribute Table, click the Add Field button (a green +).
- Give the attribute a name (e.g. "Label") and click OK. The attribute field is added.
- In the plot window, select the first object you want a label on. It is highlighted in the Attribute Table. Simply enter the attribute value you want for that object in the new field.
- Repeat step 4 for each object you want to label, just select the object and enter in the label in the Attribute Table.
- When finished, you can close the Attribute Table if you wish.
- Select the Base layer, and click the Labels tab in the Properties window.
- Set the Label source to be the attribute just created.
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Updated January 30, 2017