The best way to understand how to combine the MIN and IF functions in Excel is with an example. This tutorial example contains heat times for two events from a track meet — the 100 and 200meter sprints.
Using a MIN IF array formula allows you to find the fastest heat time for each race with one formula.
The job of each part of the formula is as follows:
 The MIN function finds the fastest or smallest time for the event chosen.
 The IF function allows us to choose the race by setting a condition using the race names.
 The array formula lets the IF function test for multiple conditions in a single cell, and when the condition is met, the array formula determines what data (race times) the MIN function examines to find the fastest time.
MIN IF Nested Formula Syntax and Arguments
The syntax for the MIN IF formula is:
=MIN( IF ( logical_test, value_if_true, value_if_false ) )
Because the IF function is nested inside the MIN function, the entire IF function becomes the sole argument for the MIN function.
The arguments for the IF function are:
 logical_test (required): a value or expression that is tested to whether it is true or false
 value_if_true (required): the value that is displayed if logical_test is true
 value_if_false (optional): the value that is displayed if logical_test is false
In the example, the logical test tries to find a match for the race name typed into cell D10 of the worksheet. The value_if_true argument is, with the help of the MIN function, the fastest time for the chosen race. The value_if_false argument is omitted since it is not needed and its absence shortens the formula. If a race name that is not in the data table, such as the 400meter race, is typed into cell D10, the formula returns a zero.
Excel's MIN IF Array Formula Example
Enter the following tutorial data into cells D1 to E9:
Race Times
Race Time (sec)
100 meters 11.77
100 meters 11.87
100 meters 11.83
200 meters 21.54
200 meters 21.50
200 meters 21.49
Race Fastest Heat (sec)
In cell D10, type "100 meters" (without the quotes). The formula looks in this cell to find which of the races you want it to find the fastest time for.
Entering the MIN IF Nested Formula
Since you are creating both a nested formula and an array formula, you need to type the entire formula into a single worksheet cell.
After you enter the formula do not press the Enter key on the keyboard or click on a different cell with the mouse; you need to turn the formula into an array formula. To do that:

Click on cell E10, the location where the formula results will be displayed.

Type the following: = MIN( IF( D3:D8=D10, E3:E8 ) )
Creating the Array Formula

Press and hold down the Ctrl and Shift keys on the keyboard.

Press the Enter key on the keyboard to create the array formula.

The answer 11.77 appears in cell F10 because it is the fastest (smallest) time for the three 100 meter sprint heats.
The complete array formula { = MIN( IF( D3:D8=D10, E3:E8 ) ) } can be seen in the formula bar above the worksheet.
Because the Ctrl, Shift, and Enter keys on the keyboard are pressed simultaneously after the formula has been typed in, the resulting formulas are sometimes referred to as CSE formulas.
Test the Formula
Test the formula by finding the fastest time for the 200 meters. Type 200 meters into cell D10 and press the Enter key on the keyboard. The formula should return the time of 21.49 seconds in cell E10.