The question is asking which rock does not belong to the same group as the others. To determine this, we need to understand the characteristics of each rock type.

1. Shale: Shale is a sedimentary rock that is made up of compressed clay, silt, and organic material. It is usually characterized by its layered structure.

2. Limestone: Limestone is also a sedimentary rock, but it is primarily composed of calcium carbonate. It often contains fossilized remains and can be found in various colors and textures.

3. Slate: Slate is a metamorphic rock that is created from the transformation of shale. It has a fine-grained texture and can be easily split into thin layers.

4. Sandstone: Sandstone is another sedimentary rock that is composed of sand-sized minerals or rock grains. It is often used as a building material due to its durability.

Based on this information, we can determine that the rock which does not belong to the same group is option 3, Slate. The other three rocks (Shale, Limestone, and Sandstone) are all sedimentary rocks, while Slate is a metamorphic rock. Therefore, it is the odd one out.