When is there always a Condorcet winner?

Question

I found the following in a book about voting systems, and it is claiming that in this particular situation there always is a Condorcet winner: "Suppose there is an odd number of voters and all voter's preferences are single peaked (ie if we identify the candidates with points on an axis and we represent by a function g the preference of a given voter then g must be either strictly increasing, decreasing, or first increasing and then decreasing, with strict preferences between the candidates), then let i be a voter whose preferred candidate is C, where C is the median or the middlemost of the preferred candidates of all voters, i is called the median-voter. Then C is the Condorcet winner". I understand why C would be a Condorcet winner but I don't understand why such a "median-candidate" C has to exist, and how do we find it? The example was taken from the book "Majority Judgement" by Laraki and Balinski, section 3.3. Thank you.