The 4 parcels on a trolley have an average mass of 15 kilograms. A fifth parcel with a mass of 5 kilograms is put on the trolley. What is the average mass of the 5 parcels?
New average = 65 ÷ 5 = 13 kg
Ans: 13 kg
How to solve it
Notice the count changes: 4 parcels, then 5. So there are two totals, one before and one after.
Find the first total from the average: 15 times 4 is 60 kilograms.
Add the new parcel to the total: 60 plus 5 is 65 kilograms.
Share the new total over the new count: 65 divided by 5 is 13 kilograms.
Check it makes sense: 13 is closer to 15 than to 5, because 4 of the 5 parcels began at 15.
When the count changes, there are two totals. One before, one after. The new average does not come from the old average. It comes from the new total.
Practice questions with worked solutions
Question 1 is free to try. The other 10 open in the free trial, each with its full working.
Question 1 of 11 · Basic · free to tryA school library lent 25, 18, 9 and 31 books from Monday to Thursday. After…A school library lent 25, 18, 9…
A school library lent 25, 18, 9 and 31 books from Monday to Thursday. After Friday, the average number of books lent per day for the five days was 22. How many books were lent on Friday?
How do you find the new average after one is added in P6?
When a value joins or leaves a group, the count changes, so there are two totals: one before and one after.
What your child learns here
When a value joins or leaves a group, the count changes, so there are two totals: one before and one after. This page teaches your child to find both totals and never to average two averages. It also covers combining two groups of different sizes.
Find the old total from the old average and count.
Add or remove a value to get the new total, then divide by the new count.
Find the combined average of two unequal groups from their totals.
Check that a new average moves only a little when one value joins a large group.
Does the answer make sense?
When one value joins a group, your child's new average must sit between the old average and that value. When two groups combine, the result must lie between their two averages and nearer the bigger group's, so the 16 bowls average between $4 and $6, closer to $4.
How to practise these questions
The Basic questions train comparing the total before and after a member joins or leaves. Intermediate questions add combining two groups of different sizes, and finding the value needed to reach a target average. Challenge questions recover a group's average from the combined one, or ask your child to judge whether a claim can be decided at all. If the change in the total is confusing, read the written step-by-step solution.
Questions parents ask
Can you average two averages? Only when the two groups are the same size. Otherwise, multiply each average by its group size, add the totals and divide by everyone together.
Why does the average change when one more value joins? Because both the total and the count change. The new average comes from the new total divided by the new count.
Which syllabus outcome covers a new average? The relationship between average, total value and number of data, outcome 1.2 under Average of a Set of Data in the Primary 6 syllabus. Finding two totals, before and after, uses that relationship twice.
