The candles in a box have an average height of 12 centimetres. One more candle, 40 centimetres tall, is put into the box. The average height of the candles becomes 16 centimetres. How many candles were in the box at first?
Candles at first = 24 ÷ 4 = 6
Ans: 6
How to solve it
Draw the candles already in the box as bars levelled at the old average, 12 centimetres, with a question mark for how many there are.
Draw the new candle, 40 centimetres tall, beside them, and a line right across the row at the new average, 16 centimetres.
Every old candle has to reach 16: 16 minus 12 is 4, so each one is 4 centimetres short. Those are the gaps.
The new candle came in at 40 but only has to stand at 16. Everything above the line is spare: 40 minus 16 is 24.
Only that spare can fill the gaps. Cut it into pieces of 4: 24 divided by 4 is 6, so the box held 6 candles.
The extra above the new average is shared out in equal pieces, and the number of pieces is the number of candles.
Practice questions with worked solutions
Question 1 is free to try. The other 12 open in the free trial, each with its full working.
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A fruit stall sold an average of 12 bunches of bananas a day over 3 days. It sold at least 8 bunches on each of the 3 days. What is the greatest number of bunches it could have sold on one day?
How do you find the number of values from an average in P6?
Some Primary 6 average questions ask for the number of data, not the average or a value.
What your child learns here
Some Primary 6 average questions ask for the number of data, not the average or a value. Your child learns to compare the old and new averages: each old value must rise to the new level, and the spare amount from the new value fills those gaps.
Find the gap each old value has to the new average.
Find the spare amount the new value has above the new average.
Divide the spare amount by the gap to find how many values there were.
Use the relationship between average, total and number of data, including floors and caps on values.
Does the answer make sense?
When the question asks how many frames, candles or passengers there were, your child's answer must be a whole number. For a greatest or lowest possible value, the answer must stay inside the stated limits, so a quiz round can score no more than 20 points and no less than 0.
How to practise these questions
The Basic questions train finding how many there were when one member joins and the average moves. Intermediate questions add whole groups joining or leaving, and limits that restrict the values. Challenge questions ask for the smallest or largest possible value, or allow more than one correct answer under a condition. If finding the count feels like guesswork, read the written step-by-step solution.
Questions parents ask
How can you find how many items there were from two averages? Compare each old value with the new average, and the new value with the new average. The spare amount above the new average fills the gaps below it, and dividing one by the other gives the count.
Why does the average only rise a little when a big value joins? Because the big value's extra is shared across every value in the new group. An extra of 10 shared among 5 old values lifts each one by only 2.
Is finding the number of data in the syllabus? It uses the relationship between average, total value and number of data, which is in the Primary 6 MOE syllabus under Statistics. Finding the number of data is one direction of that relationship.
