The BINARY GRAPH models a very efficient SEARCH method over UNIMODEL DATA. The MODE is the AVERAGE denoting the MOST FREQUENT MEASURE OF DATA. But some samples have two or more cases of equal frequency, so a sample can have more than one MODE. UNIMODAL denotes a single most frequent measure. (Example: boiling point of a chemical.)

There are two other SEARCH METHODS over UNIMODAL DATA: Fibonacci and Golden Section. They are shorter searches, but somewhat complicated to execute. BINARY SEARCH is simple, and only a "little longer".

In the MIDDLE SCHOOL Frame of this Website, I've a file, "Trapping the Wild Word", which uses BINARY SEARCH to find a designated word on a page of a dictionary of over 1000 pages, with up to 30 words defined per page. BINARY SERACH "traps" this "wild word" via ANSWERS to 15 "YES-NO" QUESTIONS -- 10 ANSWERS to determine the Page, 5 ANSWERS to determine the Word.

Here's a SEARCH PROBLEM for PRESCHOOL KIDS. 16 Numbered Boxes reside on a shelf. One Box contains "goodies"; 15 are empty. The Kid can find the Box with 4 QUESTIONS:

                                       |1 - 16|
                                       --------
                                           |
                                           |
                             "Is the Box # greater than 8?"
                                           |
                                          / \
                                         /   \
                                        /     \
                                       /       \
                                      /         \
                                     /           \
                                    /             \
                               |1-8:NO|           |9-16:YES|
                                 |                         |
                                 |                         |
                                 |                         |
                          "Than 4?"                     "Than 12?"
                           / \                                / \
                          /   \                              /   \
                         /     \                            /     \
                 |1-4:NO|   |5-8:YES|                 |9-12:NO|  |13-16:YES|
                 |                |                     |                  |
                 |                |                     |                  |
                 |                |                     |                  |
            "Than 2?"             "Than 6?"          "Than 10?"         "Than 14?"
                / \              / \                   / \                / \
               /   \            /   \                 /   \              /   \
              /     \          /     \               /     \            /     \
             /       \        /       \             /       \          /       \
      |1-2:N|    |3-4:Y|  |5-6:N|  |7-8:Y|    |9-10:N|   |11-12:Y| |13-14:N| |15-16:Y|
       |           |          |        |        |          |          |           |
       |           |          |        |        |          |          |           |
       |           |          |        |        |          |          |           |
   "Than 1?"  "Than 3?" "Than 5?"  "Than 7?"  "Than 9?"   "Than 11?" "Than 13?" "Than 15?"          / \           / \         / \        / \        / \        / \        / \        / \
  /   \         /   \       /   \      /   \      /   \      /   \      /   \      /   \
 /     \       /     \     /     \    /     \    /     \    /     \    /     \    /     \
|1N|  |2Y|  |3N|   |4Y| |5N|   |6Y| |7N|  |8Y| |9N| |10Y| |11N||12Y||13N| |14Y||15N| |16Y|

The last graph-line shows that each element of a set of 16 members is UNIQUELY DETERMINED BY A DISTINCT PATH OF THE BINARY-SEARCH GRAF.

For example, suppose the "goodies" were in Box 11. This is UNIQUELY DETERMINED by the 4-QUESTION PATH: |greater than 9:YES| Þ |greater than 12:NO| Þ |greater than 10:YES| Þ |greater than 11:NO|. Similar BINARY-SEARCHES can UNIQUELY DETERMINE THE UNIMODE OF ANY UNIMODAL DISTRIBUTION, whether an ITEM, a MEASURE, or whatever.