The numbers of books read in a month by seven members of a reading club are 3, 5, 7, 7, $x$, 9 and 10, and for this data the mean equals the mode. What is $x$?

Explanation

1. 01

   If $x$ equals 3, 5, 9 or 10 there would be two modes, so the single mode is 7.

2. 02

   Mean = 7 means the total is $7 \times 7 = 49$.

3. 03

   The other six values add to 41, so $x = 49 - 41 = 8$.

4. 04

   Check: 8 does not create a tie, so the mode stays 7.