Range of Most Common Values I have a few numbers such as:

24
  65
  62
  63
  39
  52
  88
  21
  65
  65
  62
  75

Using Excel, I am looking to identify a range of numbers whose maximum and minimum are not more than 10% different from one another, and subsequently find the range that contains the most numbers (i.e. the modal range).
The 10% difference would be defined by $$(\max-\min) \le 0.1(\max+\min)/2.$$ 
 A: Problem statement
Let the $n$ numbers be sorted so they can be written
$$x_1 \le x_2 \le \cdots \le x_n.$$
Using $2\lambda$ as a general name for the 10% value, we seek an interval of the form $[x_t, x_{t+k}]$ where
$$x_{t+k} - x_t \le \lambda \left(x_t + x_{t+k}\right)$$
and $k$ is as large as possible.
Solution
That criterion is algebraically equivalent to
$$x_{t+k} \le \frac{1+\lambda}{1-\lambda}x_t.$$
Thus, all one has to do is compute the multiples of the data $\mu x_t$ for $\mu = \frac{1+\lambda}{1-\lambda}$ and count how many lie within each interval of the form $[x_t, \mu x_t]$.

Excel implementation
Arrange the data in a column and sort them in ascending order.  To illustrate, I put them in column A beginning at the second row.
In a parallel column (such as column B), multiply the values by $\mu$.
In another parallel column, count the intervals using COUNTIF.  The expressions in the example look like
=COUNTIF(A2:A$100, "<=" & B2)
=COUNTIF(A3:A$100, "<=" & B3)
...
=COUNTIF(A13:A$100, "<=" & B13)

Find the largest value(s) in this column: they are next to the desired intervals.

This is what the formulas look like:

Data is the range A2:A13 containing the sorted values.  Indicator is the range under the heading "Mode"; its non-blank values show where the modal intervals begin.  Idx (short for "Index", which is a reserved word for Excel), Lambda, and Mu are cells just to the right of the corresponding names.
(I apologize that the illustrated value for $\lambda$ is twice that requested in the question.)
