expected value for non numerals

The problem statement is from here https://brilliant.org/practice/information-asymmetry/?p=2

You pick a random card (all are equally likely) from a deck of cards numbered 1, 2, 3, ..., 49 and see that your card is 15. Your friend knows you picked a random card, but doesn't know which one. What is the expected value of the number on your card to your friend?

Given explanation is:

Even though you know that your card is the 15, and thus to you the expected (and certain) value is 15, your friend doesn't know this. So, in order to find the expected value, he knows that all the cards were equally likely, so he can average (1+⋯+49)/49 = 25 as the expected value of your card.

My question how can we average the numbers 1 to 49? From my point of view they should be treated as categories, for ex: If we use a different deck of 10 cards each with a picture of unique fruit and we want to find the expected fruit after shuffling and picking a random card then we can't add all the fruits and divide by 10, can we?

Note by Bharat To
1 year, 8 months ago

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