Correct spelling, explanation: shown is the past participle form of the verb to show. Shown is a word with a long history as it could already be found in Old English, but back then it had the form sceawian and it meant to inspect or look at. Later, the word also appeared in Dutch and German and then shown started to look the way we know it today.

Definition of shown:
1. verb (past participle) – to make something be seen,
On the map urban areas are shown in red color so you can clearly see that the country is highly urbanized.
2. verb (past participle) – to express something,
He has shown his strong emotions by screaming and slamming the door.
3. verb (past participle) – to explain something to somebody,
It’s my first day at work so I feel quite stressed, but luckily, my colleague has shown me how to operate all the machines.

Collocations with shown:
A few common collocations with shown include: shown somebody in; shown somebody the way, and shown somebody around.
John has just shown me the project so we can immediately get down to work.
He has shown me the way to school a few times, but I still don’t remember it.
Julia has shown me around her house, which is really impressive.

Incorrect spelling, explanation: the verb show is irregular and its past participle form can be either showed or shown. Probably because of that, a number of English speakers mix those forms and a common mistake is to spell shown as showed, which of course is incorrect.