Standard British university marks

Standard marks end in 2, 5, or 8, and a triple of them define a grade class:

mark	UG classification	PG classification
78	First Class Honours 1st	Distinction
75
72
68	Second Class Honours Upper Division 2:1	Merit
65
62
58	Second Class Honours Lower Division 2:2	Pass
55
52
48	Third Class Honours 3rd	Fail
45
42
38	Fail
35
32

The average step size of marks ending in 2, 5, or 8 is is 10/3, and they can be enumerated by
\[ m_i = \left [ \frac{5}{3} + \frac{10}{3} ~ i \right ], \]
where the brackets indicate rounding to the nearest integer, standard marks correspond to indices \(i = 9, 10, …, 23\), and \(i = 0, …, 29\) covers the range from 0 to 100 (2 to 98).

If an assigment has been marked by a point system, \(p = 0, 1, …, p_\mathup{max}\), and points should be converted to marks ending in 2, 5, or 8, this can be achieved by the function
\[ m(p) = \left [ \frac{5}{3} + \frac{10}{3} ~ \left [ \frac{p}{p_\mathup{max}} i_\mathup{max}\right ] \right ], \]
where \(i_\mathup{max}\) is the index of the mark which should be assigned to a perfect result, \(p = p_\mathup{max}\), e.g. \(i_\mathup{max} = 25\) for a maximum mark of 85. In Excel formula notation:

=ROUND((5 + 10 * ROUND(P / P_MAX * I_MAX, 0)) / 3, 0)

P should be replaced by the field containing the points and P_MAX & I_MAX by constants.