Excel - Find the biggest gap in a set of numbers? - excel

Question

I have a series of numbers
0,1,99,5,5,98,9
They are unsorted and will remain that way.
I cannot use macros.
I want the answer 89 from a formula or an array formula.
89 is the biggest gap (between 9 and 98) in this series when sorted.
I want a formula, no vba, and no sorting my column or row.
I need a formula that sorts the list and subtracts one cell relative to the sorted list and gives the largest difference of the list of differences it creates.
so the list becomes 0,1,5,5,9,98,99
subtracts the current from the previous (na,1,4,0,4,89,1)
and gives me the max 89.
My list is a column of 7 rows.

Answer 1

This formula must be array-entered. In the formula RNG refers to the range where you have entered your numbers, e.g. A1:A7
=MAX(LARGE(RNG,ROW(INDIRECT("1:"&-1+COUNT(RNG))))-
LARGE(RNG,ROW(INDIRECT("2:"&COUNT(RNG)))))
To array-enter a formula, after entering
the formula into the cell or formula bar, hold down
ctrl-shift while hitting enter. If you did this
correctly, Excel will place braces {...} around the formula.
You can see how the formula works by using the Evaluate Formula option on the Formula Auditing tab of the Formulas ribbon.
In brief, the formula works by creating two arrays, sorted in order of size. The "K" value of the LARGE function is an array created by the ROW(INDIRECT sequence. The first returns
{1;2;3;4;5;6}
and the second returns
{2;3;4;5;6;7}
The two arrays of values returned would then be:
{99;98;9;5;5;1}
{98;9;5;5;1;0}
Subtracting one from the other results an array of the differences, and we find the MAX.

Answer 2

MAX(A:A) - LARGE(A:A,2) gives the difference between the largest and second-largest value if your numbers are in column A. Don't put this formula in column A.

Answer 3

Place the values in A1 thru A7 in any order!
In B1 enter:
=RANK(A1,$A$1:$A$7,0)+COUNTIF($A$1:$A1,A1)-1
and copy down thru B7
In C1 enter:
=INDEX($A$1:$A$7,MATCH(ROW(),B$1:B$7,0))
and copy down thru C7
In D2 enter:
=C1-C2
and copy down thru C7
Finally in E1 enter:
=MAX(C:C)
Column B represents the order of the values in column A if they were sorted. Column C contains the values of column A in sorted order. Column D are the differences and E1 gives the desired answer. Here is an example: