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How about removing the hour?

awk -F'|' 'NR>2 {array[$1] += $3 count[$1]++ } END { for (a in array) {print a, array[a]/count[a] } } '

Unlike many languages where two adjacent strings representing numbers separated by a space would be a syntax error, awk is happy to concatenate them and treat them as a single numeric string.

So...

I understand the concatenation but what I'm not getting is why the extra digits being added are off by one for each line. For example, for line 3, I would expect the extra digit in red to be 1...

I have only tested this with the given data, but I'm surprised that you're showing sample output that includes the data marked in red above when there was no sample input for that date. When I tried...

Don,
Yes, I added another test record with 3/3/2015 date to test the break logic and forgot to remove it from posted output (as OP did not include it in his file). I missed the semi-colon although...