A purse holds three ₹5 coins and two ₹10 coins. One coin is taken out at random. What is the expected value of the coin taken out, in ₹?

An expected value weights each possible value by its probability: (3/5)(5) + (2/5)(10) = 3 + 4 = ₹7. The plain average of the two coin values, (5 + 10)/2 = ₹7.50, would be right only if the two kinds of coin were equally likely; here the cheaper coin is the commoner one, so the answer must fall below ₹7.50. The value ₹5 is the commonest coin, that is the mode, and ₹10 the largest. Note that ₹7 is not the value of any single coin — an expected value is a long-run average, not a possible outcome.