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The average, or arithmetic mean, of a set of numbers is the total divided by the number of values. Identify exactly which values belong in the set before calculating. The divisor is the count of those values, not the largest number or the number of different values.
This Primary 6 Mathematics guide connects average with equal sharing, reconstructs totals and solves one missing-value example. It uses original hypothetical counts and measurements. The topic here is an arithmetic mean of comparable values, not average speed or a general rule for every situation called an average.
Valour Primary's 2026 Mathematics overview includes average in its P6 routes. MOE's Mathematics syllabus updated October 2025 is the national reference; its direct download presented a verification screen. These are original teaching exercises, not official exam questions or a complete syllabus audit. Standard and Foundation learners should follow their applicable school scope.
Imagine three boxes containing 6, 9 and 12 counters. Their total is 27 counters. If that total were shared equally among the three boxes, each would contain 9 counters. The average count is therefore 27 ÷ 3 = 9.
The original boxes do not have to contain equal amounts. The average describes the equal-share value of their combined total. It does not claim that the counters were actually moved between boxes.
For 4, 4 and 10, the total is 18 and there are three values. Average = 18 ÷ 3 = 6. The repeated four still counts twice because it describes two entries.
Do not divide by two because only two different numbers appear. Likewise, include a recorded zero when it is one of the values in the defined set. Removing it changes the set and may change the average.
Three ribbons have lengths of 8 cm, 11 cm and 14 cm. Total length = 33 cm. Average length = 33 ÷ 3 = 11 cm. The average retains the length unit.
If measurements use different units, convert them to a common unit first. Do not add 1 metre and 20 centimetres as though the total were 21 centimetres. Identify what is being averaged and keep that quantity consistent.
Four packets have an average of 7 stickers each. Their combined total is 7 × 4 = 28 stickers. Multiplying the average by the number of values reverses the original total-divided-by-count calculation.
This information does not prove that each packet contains seven stickers. The distribution may differ while the total stays 28. Use the average to recover a total, not to invent individual contents.
Three reading sessions average 20 minutes. Two sessions lasted 15 and 18 minutes. The total duration of all three sessions is 20 × 3 = 60 minutes. The known total is 15 + 18 = 33 minutes.
The missing duration is 60 − 33 = 27 minutes. Check: (15 + 18 + 27) ÷ 3 = 20 minutes. Do not subtract the known durations directly from 20; twenty is the average, not the total.
Two bags average 10 marbles each, so their total is 20. A third bag contains 18 marbles. The combined average is (20 + 18) ÷ 3 = 12⅔ marbles per bag.
The result need not be a whole number even though individual bags hold whole marbles. Do not average 10 and 18 directly: those figures represent groups of different sizes. Recover each group's total and divide by the combined item count.
- Find the average of 5, 8 and 11.
- Find the average of 0, 6 and 6.
- Five boxes average 8 counters each. Find the total.
- Three values average 12. Two values are 9 and 14. Find the third.
- Two jars average 6 beads each. A third jar has 9 beads. Find the average for all three jars.
Answers: 1. 8. 2. 4, because all three entries count. 3. 40 counters. 4. Total 36; known total 23; missing value 13. 5. (12 + 9) ÷ 3 = 7 beads per jar.
For a non-empty set of ordinary numerical values, its mean lies between the smallest and largest values, including those endpoints. An answer outside that range indicates a calculation or set-selection error. This check does not replace the full calculation.
Label total, count and average in working. If the method is uncertain, return to three small groups of counters and the equal-sharing explanation before adding missing values or combined groups.