How to get an array formula to work both vertically and horizontally?

Try this array formula instead:

=INDEX(_Reports[Grade],MATCH(ROUNDDOWN(AVERAGE(IF(TRANSPOSE(D4:D7)=_Reports[Grade],_Reports[Score])),0),_Reports[Score],0))

For the columns, you need to transpose the lookup arrays:

=INDEX(_Reports[Grade],MATCH(ROUNDDOWN(AVERAGE(IF(D4:D7=TRANSPOSE(_Reports[Grade]),TRANSPOSE(_Reports[Score]))),0),TRANSPOSE(_Reports[Score]),0))

Which one of us are you addressing? You have been offered two solutions.

Use the Evaluate Formula option on the Formulas ribbon to step through it so you can see what is happening. Essentially in mine, because you were working with rows in the main table and columns in the lookup table, you need to switch this when you want to work with columns in the main table. TRANSPOSE simply turns the lookup arrays 90 degrees to facilitate this.

I've answered your question above.

Glenn's approach is the same, but he's chosen to transpose the main table column instead. Essentially, one or other of the arrays needs transposing.

Does this answer your question?

In your original (working) formula, the construction of the formula meant that you were multiplying two arrays. One (sheet 1) was a horizontal array, and the other (Codes) was a vertical array. When multiplied together they produced a 4 x 15 array of TRUE/FALSE responses.

In your original (non-working) formula, the two arrays were vertical. When multiplied together The first four rows of the codes array were searched for the 4 values in sheet 1. the remaining 11 rows of codes produced an error and the formual fell over. To get it to work, you had to coerce Excel to make one of the arrays horizonatal. That's what TRANSPOSE does.

Glad to have helped.