Find the range, then assign grade bands

Instead of dividing the class into above and below average, we can create four grade bands. First discover the lowest and highest actual Mathematics marks. Only then can we set fixed bands and classify students.

Update minimum and maximum independently #

Minimum = 101
Maximum = -1
for each row X in Scores {
    if (X.Mathematics < Minimum) { Minimum = X.Mathematics }
    if (X.Mathematics > Maximum) { Maximum = X.Mathematics }
}

These initial values work because valid marks lie from 0 to 100. The first value, 68, updates both variables. Use two separate if statements, not if / else. Starting both variables from the first real row is another safe approach for a nonempty dataset.

Count integer values, including both ends #

Maximum − Minimum = 97 − 42 = 55 is the numerical difference. There are 97 − 42 + 1 = 56 possible integer marks when both ends are included. Four equal groups of 14 integer values give the following bands.

for each row X in Scores {
    if (X.Mathematics >= 84) { Grade = "A" }
    else if (X.Mathematics >= 70) { Grade = "B" }
    else if (X.Mathematics >= 56) { Grade = "C" }
    else { Grade = "D" }
    record (X.CardNo, Grade)
}

These are the lecture’s example bands, not an official grading policy. Equal-width intervals do not promise equal student counts. Boundary choices must be explicit; a new dataset may require different bands. If min equals max, handle that separately rather than pretending there is a spread.