Reasoning about data – practice for Years 5–9

Sample questions on Reasoning about data with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject

Maths

Year

Years 5–9

Curriculum area

Relationships, functions and data

Question types: True statements about data

Sample questions

1. Question 1 Easy

   Class A has 23 pupils, class B 26 pupils and class C 29 pupils. Decide whether each statement is true (YES) or not (NO).

   1. The pupils of class C can be split into groups of 6 with nobody left over.
   2. There are 81 pupils in the three classes together.
   3. There are 4 more pupils in class B than in class A.
   4. There are 8 more pupils in class C than in class A.
   Show the solution

   Answer:

   1. The pupils of class C can be split into groups of 6 with nobody left over. – no
   2. There are 81 pupils in the three classes together. – no
   3. There are 4 more pupils in class B than in class A. – no
   4. There are 8 more pupils in class C than in class A. – no

   How it works: Together 23 + 26 + 29 = 78, mean 78 ÷ 3 = 26; differences 3, 3, 6.

2. Question 2 Normal

   Class A has 20 pupils, class B 25 pupils and class C 27 pupils. Decide whether each statement is true (YES) or not (NO).

   1. The pupils of class B can be split into groups of 5 with nobody left over.
   2. On average there are 26 pupils in a class.
   3. There are 9 more pupils in class C than in class A.
   4. There are 71 pupils in the three classes together.
   Show the solution

   Answer:

   1. The pupils of class B can be split into groups of 5 with nobody left over. – yes
   2. On average there are 26 pupils in a class. – no
   3. There are 9 more pupils in class C than in class A. – no
   4. There are 71 pupils in the three classes together. – no

   How it works: Together 20 + 25 + 27 = 72, mean 72 ÷ 3 = 24; differences 5, 2, 7.

3. Question 3 Hard

   Class A has 26 pupils, class B 30 pupils and class C 28 pupils. Decide whether each statement is true (YES) or not (NO).

   1. The pupils of class B are more than a third of all the pupils.
   2. The pupils of class C can be split into groups of 4 with nobody left over.
   3. On average there are 28 pupils in a class.
   4. There are 5 more pupils in class B than in class A.
   Show the solution

   Answer:

   1. The pupils of class B are more than a third of all the pupils. – yes
   2. The pupils of class C can be split into groups of 4 with nobody left over. – yes
   3. On average there are 28 pupils in a class. – yes
   4. There are 5 more pupils in class B than in class A. – no

   How it works: Together 26 + 30 + 28 = 84, mean 84 ÷ 3 = 28; differences 4, 2, 2.

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