Based on the stated requirements... I think this is what you're looking for...

IF OBJECT_ID('tempdb..#temp') IS NOT NULL

DROP TABLE #temp;

CREATE TABLE #temp([term] int,

[course] varchar(10),

[mark] float);

INSERT INTO #temp (term,course,mark) VALUES

(1,'math',3),

(1,'eng',4),

(1,'hist',4.5),

(1,'anth',4.5),

(2,'comp',3),

(2,'math',4),

(2,'bio',4.5),

(2,'chem',4.5),

(3,'soc',4.5),

(3,'math',4.5),

(3,'bio',4),

(3,'chem',4);

WITH NewMark AS (

SELECT

t.term,

CASE WHEN t.mark = MAX(t.mark) OVER (PARTITION BY t.course ORDER BY t.course, t.term) THEN t.mark END AS NewMark

FROM

#temp t

), AvgPrep AS (

SELECT

nm.term,

COUNT(nm.NewMark) * 1.0 AS CourseCount,

SUM(nm.NewMark) * 1.0 MarkSum

FROM

NewMark nm

GROUP BY

nm.term

)

SELECT

ap.term,

SUM(ap.MarkSum) OVER (ORDER BY ap.term) / SUM(ap.CourseCount) OVER (ORDER BY ap.term) AS RunningAvg

FROM

AvgPrep ap

Here are the results...

term RunningAvg

----------- ----------------------

1 4

2 4

3 4.1