Enum-like menu to display list elements?

I really like how Enum’s are displayed in the inspector: ie, you can click the field, see a drop down of all possible options, and select one.

I’m wondering if its possible to display a list in this fashion?

using UnityEditor;
using System.Collections.Generic;

[CustomEditor(typeof(StatList))]
public class StatListEditor: Editor
{
    public List<string> statList = new List<string>()
    {
        "hp", "mp", "str", "lck", "dmg"
    };

    public int selectedIndex = 0;

    public override void OnInspectorGUI()
    {
        serializedObject.Update();

        EditorGUILayout.PrefixLabel("Attributes");

        selectedIndex = EditorGUILayout.Popup(selectedIndex, statList.ToArray());

        serializedObject.ApplyModifiedProperties();
    }
}

What do I do if the list for which I want to create a dropdown menu (which will be visible in the “StatList” script) is found in the “StatList” script itself and not in the “StatListEditor” script editor?