Totalling, Counting, Max, Min & Average

🎯 Syllabus & Goals 3 min

Cambridge 7.4 · Standard methods of solution Paper 2 · Algorithms, Programming and Logic

By the end of this lesson you can:

1. Write the standard methods for totalling and counting, including counting down.
2. Find the maximum and minimum of a list using both initialisation methods.
3. Calculate an average (mean) from a total, and trace all of these in a trace table.

Textbook: Chapter 7, §7.4.1–7.4.3 (pp. 272–274)

Recap / Warm-Up 5 min

You can now write assignment, selection and all three loops. Standard methods are small, reusable patterns built from exactly those parts. Real programs repeat them thousands of times.

Quick starter

Which loop would you use to process every mark in a class of 30 — and why?

🧠 Key Concept 14 min

1 · Totalling

Totalling keeps a running total that each value is added to. The total must start at zero before the loop.

Total ← 0
FOR Counter ← 1 TO ClassSize
  Total ← Total + StudentMark[Counter]
NEXT Counter

2 · Counting

Counting keeps a count of how many times something happens. It adds 1, not the value. It is often inside an IF, so only some items are counted.

PassCount ← 0
FOR Counter ← 1 TO ClassSize
  IF StudentMark[Counter] >= 50
    THEN
      PassCount ← PassCount + 1
  ENDIF
NEXT Counter

NumberInStock ← NumberInStock - 1
IF NumberInStock < 20
  THEN
    CALL Reorder()
ENDIF

3 · Maximum, minimum and average

To find the largest value, keep a "best so far" and replace it whenever a larger value appears. The smallest works the same way the other way round. There are two ways to start:

The average (mean) extends totalling: total everything inside the loop, then divide by the number of values after the loop: Average ← Total / ClassSize.

Worked Example 12 min

Worked example 1 · Total, count of passes and average

Six students scored 45, 62, 38, 71, 55, 59 (stored in Score[1] to Score[6]). Output the total, the number of scores of 50 or more, and the average.

DECLARE Score : ARRAY[1:6] OF INTEGER
Total ← 0
PassCount ← 0
FOR Counter ← 1 TO 6
  Total ← Total + Score[Counter]
  IF Score[Counter] >= 50
    THEN
      PassCount ← PassCount + 1
  ENDIF
NEXT Counter
Average ← Total / 6
OUTPUT Total, " ", PassCount, " ", Average

score = [45, 62, 38, 71, 55, 59]
total = 0
pass_count = 0
for counter in range(6):
    total = total + score[counter]
    if score[counter] >= 50:
        pass_count = pass_count + 1
average = total / 6
print(total, pass_count, average)

330 4 55.0

1. Initialise both to 0 before the loop.otherwise the first addition uses an unknown value.
2. Every pass adds to Total; only passes where the score is ≥ 50 add 1 to PassCount (passes 2, 4, 5, 6).
3. After the loop, Average ← 330 / 6 = 55.dividing inside the loop would give a wrong "average so far" every pass.
4. Python note: lists start at index 0, so range(6) gives 0–5. Pseudocode's array here runs 1–6. Same six items, different numbering.

Worked example 2 · Highest and lowest score (Method B)

MaximumScore ← Score[1]
MinimumScore ← Score[1]
FOR Counter ← 2 TO 6
  IF Score[Counter] > MaximumScore
    THEN
      MaximumScore ← Score[Counter]
  ENDIF
  IF Score[Counter] < MinimumScore
    THEN
      MinimumScore ← Score[Counter]
  ENDIF
NEXT Counter
OUTPUT MaximumScore, " ", MinimumScore

score = [45, 62, 38, 71, 55, 59]
maximum_score = score[0]
minimum_score = score[0]
for counter in range(1, 6):
    if score[counter] > maximum_score:
        maximum_score = score[counter]
    if score[counter] < minimum_score:
        minimum_score = score[counter]
print(maximum_score, minimum_score)

71 38

1. Both start at the first score, 45.a value from the list can never be "beaten" by an impossible starting value.
2. The loop starts at 2, because item 1 is already the best so far.
3. Two separate IFs, not IF…ELSE. Each score is checked against both the maximum and the minimum.with ELSE, a score that set a new maximum would skip the minimum test — harmless here, but a bad habit.
4. Result: maximum 71, minimum 38.

Try It Yourself 12 min

📝 Exam Practice 10 min

Count ← 0
Big ← 0
FOR N ← 1 TO 4
  INPUT X
  IF X > 10
    THEN
      Count ← Count + 1
  ENDIF
  IF X > Big
    THEN
      Big ← X
  ENDIF
NEXT N
OUTPUT Count, Big

🗝️ Recap & Key Terms 3 min

Totalling adds each value to a total that starts at 0. Counting adds 1 each time something happens. Maximum and minimum keep a "best so far", starting either at extreme values or at the first item. The average is the total divided by the number of values, after the loop.

Totalling

Keeping a running total that values are added to, e.g. Total ← Total + Mark.

Counting

Keeping a count of the number of times an action is performed, e.g. Count ← Count + 1.

Initialisation

Giving a variable its starting value before it is used, e.g. Total ← 0.

Maximum / minimum

The largest / smallest value in a list, found by comparing each item with the best so far.

Average (mean)

The total of the values divided by how many values there are.

Homework 1 min

Task (≤ 15 min): A shop records the number of items sold each day for 30 days in Sales[1:30]. Write pseudocode to output the highest sales, the lowest sales, the average, and how many days sold more than the average. [6]

Total ← 0
Highest ← Sales[1]
Lowest ← Sales[1]
FOR Day ← 1 TO 30
  Total ← Total + Sales[Day]
  IF Sales[Day] > Highest
    THEN
      Highest ← Sales[Day]
  ENDIF
  IF Sales[Day] < Lowest
    THEN
      Lowest ← Sales[Day]
  ENDIF
NEXT Day
Average ← Total / 30
AboveCount ← 0
FOR Day ← 1 TO 30
  IF Sales[Day] > Average
    THEN
      AboveCount ← AboveCount + 1
  ENDIF
NEXT Day
OUTPUT Highest, " ", Lowest, " ", Average, " ", AboveCount