Explanation
The MEDIAN function has no built-in way to apply criteria. Given a range, it will return the MEDIAN (middle) number in that range.
To apply criteria, we use the IF function inside MEDIAN to “filter” values. In this example, the IF function filters by group like this:
IF(group=E5,data)
This expression compares each value in the named range “group” against the value in E5 (“A”). Because the criteria is applied to an array with multiple values, the result is an array of TRUE FALSE values like this:
{TRUE;TRUE;TRUE;TRUE;TRUE;FALSE;FALSE;FALSE;FALSE;FALSE}
In this array each TRUE corresponds to a value in group A. The IF function evaluates these results and returns the corresponding value from the named range “data”. The final result from IF is
{1;2;3;3;5;FALSE;FALSE;FALSE;FALSE;FALSE}
Notice only values in group A have survived, and group B values are now FALSE. This array is returned to the MEDIAN function, which automatically ignores FALSE values and returns median value, 3.
Note: when IF is used this way to filter values with an array operation, the formula must be entered with control + shift + enter.
Additional criteria
To apply more than one criteria, you can nest another IF inside the first IF:
{=MEDIAN(IF(criteria1,IF(criteria2,data)))}
To avoid extra nesting, you can also use boolean logic in the criteria .
Explanation
The MODE function has no built-in way to apply criteria. Given a range, it will return the most frequently occurring number in that range.
To apply criteria, we use the IF function inside MODE to filter values in a range. In this example, the IF function filters values by group with an expression like this:
IF(group=E5,data)
This compares each value in the named range “group” against the value in E5, which is “A”. Because the logical test is applied to an array with multiple values, the result is an array of TRUE FALSE values:
{TRUE;FALSE;TRUE;FALSE;TRUE;FALSE;TRUE;FALSE;TRUE;FALSE}
where each TRUE corresponds to a row where the group is “A”. This array becomes a filter. For each TRUE, IF returns the corresponding value in the named range “data”. FALSE values remain unchanged. The final result of IF is this array:
{3;FALSE;3;FALSE;5;FALSE;1;FALSE;2;FALSE}
Notice only values in group A have survived, group B values are now FALSE. This array is returned to the MODE function, which automatically ignores FALSE values and returns the most frequently occurring number, which is 3.
Note: when IF is used this way to filter values with an array operation, the formula must be entered with control + shift + enter.
Additional criteria
To apply more than one criteria, you can nest another IF inside the first IF:
{=MODE(IF(criteria1,IF(criteria2,data)))}
