How to spell STAIEDOUT correctly?

If you meant "stayed out", then the correct spelling is with a "y". Alternatively, "stayed outside" can be an appropriate phrase. If it is a proper noun, perhaps it should be "Staedtler" or "Staunton", depending on the context.

• stakeout The police team was on a stakeout, waiting for the suspect to arrive at the scene.
• standout Her unique style and creativity made her a standout in the fashion industry.

Attenttion

• attention
• attentions
• attenuation
• inattention