The table shows the mass of newspaper collected in each of 5 weeks, in kilograms: 45 in Week 1, 30 in Week 2, 35 in Week 4 and 28 in Week 5. The average mass collected each week was 36 kilograms. What was the mass of newspaper collected in Week 3?
Week 3 = 180 − 138 = 42 kg
Ans: 42 kg
How to solve it
Draw every week as a bar, including the week with the question mark. There are 5 weeks, so 5 bars.
The average is the level height, so 1 unit is 36 kilograms.
Find the total: there are 5 units, and 36 times 5 is 180.
Add the weeks you know: 45 plus 30 plus 35 plus 28 is 138.
What is left of the total is the missing week: 180 minus 138 is 42 kilograms.
A week with no number is still a week. Go through the total, and the missing one is what's left.
Practice questions with worked solutions
Question 1 is free to try. The other 9 open in the free trial, each with its full working.
Question 1 of 10 · Basic · free to tryRavi threw three darts. His average score for the three throws was 47…Ravi threw three darts. His…
Ravi threw three darts. His average score for the three throws was 47 points. His first throw scored 39 points, and his second and third throws scored the same number of points each. How many points did each of his second and third throws score?
How do you find a missing number from an average in P6?
When the average is given and one value is missing, your child goes through the total: average times number of data gives the total, and the missing value is what is left after the known values come off.
What your child learns here
When the average is given and one value is missing, your child goes through the total: average times number of data gives the total, and the missing value is what is left after the known values come off. This uses the relationship between average, total and number of data.
Find the total from the average and the number of data.
Count the missing value as one of the data.
Minus the known values from the total to find the missing one.
Share what is left between two equal unknowns when a question says they are the same.
Does the answer make sense?
The missing value must balance the known ones around the average: if the known values fall short of the average overall, the missing one your child finds must sit above it, and the other way round. A rainy Monday with $0 takings, for example, forces Friday's takings well above the average.
How to practise these questions
Basic questions train going through the total: average times count, then subtract the known values. Intermediate questions add a zero inside the data and values linked by a multiple. Challenge questions use two values whose sum alone is known, three linked unknowns, or an average of only some of the values. When a missing value will not appear, read the written step-by-step solution together.
Questions parents ask
How do you find a missing number when you know the average? Multiply the average by the number of data to find the total, then minus the values you know. What is left is the missing value.
Should the missing value be counted in the number of data? Yes. A value with no number yet is still one of the data. If there are 5 weeks and one is missing, the total is the average times 5.
Which syllabus outcome covers a missing number from an average? It uses the relationship between average, total value and number of data, outcome 1.2 under Average of a Set of Data in the MOE Primary 6 syllabus.
