Data questions ask your child to read a graph or table, summarise it or find a chance, after deciding which group counts. Your child is tested at their current year level, and each school selects its own test date.
Reading graphs and tables, summarising what they show, and reasoning about chance. Data is the last area in Edutest's description of Mathematics: year-level maths: numbers, measurement, algebra, space and data.
Our questions are written for children in Years 6–7 applying for Year 7 or 8. At that level, your child reads column graphs, line graphs, dot plots and tables, and finds the mean, median, mode and range. They also find what percentage of a group did something, and give a probability as a fraction from 0 to 1.
In our questions the numbers are small. What each one really tests is reading: which column, which group and which total.
They're four different summaries, and each has its own slip to check for. Under time pressure the words blur, so have your child say how each one is found before the test, not during it.
In a frequency table, the median is the middle person, not the middle row. Your child counts down the table, adding the frequencies, until reaching the middle position.
The four summaries
Measure
How to find it
The usual slip
Mean
Add every value, then divide by how many values there are
Dividing by the wrong count
Median
Put the values in order and take the middle
Not ordering first, or missing that an even list has two middles
Mode
The value that appears most often
Giving how often it appears instead of the value
Range
Largest value minus smallest
Using the first and last values as they are listed
How should your child work a data question?
Read the picture first, then the question, then find the total. This order works because a percentage or a probability is a part over a total, and the total is where a misread question shows up.
Read the title, labels and scale
Check what each bar or row stands for, and what each gridline is worth, before reading any value.
Find the group the question means
Everyone, or only those who didn't choose canoeing? Look for the words that set the group.
Write the total for that group
A percentage or a probability is a part over this total, so the total has to be right.
Check the answer against the picture
A tall bar should give a large share. If the answer says otherwise, recheck the total.
Four worked examples
Our four examples follow the Edutest style and mix easier and harder questions. Each one shows the answer and the working. Read them with your child, and for each ask what the total was and where it came from.
Then ask which option looked right at first, and compare its total. A wrong total means the group was misread; a right total with a wrong option means a slip in the working.
Worked explanation 1
A bag holds 5 lemon, 7 lime and 8 orange lollies. Noah eats one orange lolly. Then Mia takes one of the lollies left without looking. What is the probability that Mia's lolly is not orange?
AA.
7/19
BB.
11/19
CC.
3/5
DD.
12/19
Answer: D
Answer: D (12/19)
After Noah eats one, 19 lollies are left: 5 lemon, 7 lime and 7 orange. Not orange means lemon or lime, and none of those were eaten: 5 + 7 = 12. So the probability is 12/19.
The trap: 3/5 tempts children who forget that one lolly has gone. 12 out of 20 is 3/5, but only 19 lollies are left to choose from.
Why the other options are wrong
A (7/19): 7/19 is the chance that Mia's lolly is orange.
B (11/19): Takes the eaten lolly away from the lemon and lime lollies instead of the orange ones.
C (3/5): Uses all 20 lollies, forgetting the one Noah ate.
Worked explanation 2
The column graph shows the main activity chosen by each student at a school camp: Canoeing 15, Archery 7, Climbing 10 and Orienteering 8. Every student chose exactly one activity. Of the students who did not choose canoeing, what percentage chose climbing?
Main activity chosen at camp (number of students)
Canoeing
15
Archery
7
Climbing
10
Orienteering
8
·
AA.
10%
BB.
25%
CC.
40%
DD.
60%
Answer: C
Answer: C (40%)
Only the students who did not choose canoeing count: 7 + 10 + 8 = 25 students. Climbing is 10 of these 25, and 10/25 = 40/100 = 40%.
The trap: 25% tempts children who compare climbing with every student at the camp: 15 + 7 + 10 + 8 = 40 students, and 10/40 = 25%. The question is only about the 25 who did not choose canoeing.
Why the other options are wrong
A (10%): Writes the 10 climbers straight down as 10%.
B (25%): Divides by all 40 students instead of the 25 who did not choose canoeing.
D (60%): 60% is the share of those 25 who chose archery or orienteering (15 out of 25).
Worked explanation 3
Twenty-five students were asked how many brothers and sisters they have. The table shows the results: 4 students have 0, 9 have 1, 7 have 2, 3 have 3 and 2 have 4. What is the median number of brothers and sisters?
Brothers and sisters
Number of students
0
4
1
9
2
7
3
3
4
2
AA.
1
BB.
1.6
CC.
2
DD.
7
Answer: A
Answer: A (1)
Line up all 25 students in order of their answers. The median is the middle student, the 13th. Students 1 to 4 have 0, and the next 9 (students 5 to 13) have 1. So the 13th student has 1, and the median is 1.
The trap: 2 tempts children who take the middle of the first column (0, 1, 2, 3, 4) instead of the middle student.
Why the other options are wrong
B (1.6): 1.6 is the mean: 40 brothers and sisters shared among 25 students.
C (2): 2 is the middle of the list 0 to 4, not the middle student.
D (7): 7 is the middle number in the 'Number of students' column.
Worked explanation 4
A two-digit number from 10 to 99 is chosen at random. What is the probability that its tens digit is larger than its ones digit (as in 52 or 90)?
AA.
2/5
BB.
9/20
CC.
1/2
DD.
5/9
Answer: C
Answer: C (1/2)
There are 99 − 10 + 1 = 90 two-digit numbers. Count by tens digit: tens digit 1 gives 1 number (10), tens digit 2 gives 2 (20, 21), tens digit 3 gives 3, and so on up to tens digit 9, which gives 9. That is 1 + 2 + … + 9 = 45 numbers, so the probability is 45/90 = 1/2.
The trap: 2/5 tempts children who forget that the ones digit can be 0. Leaving out 10, 20, …, 90 gives only 36 numbers, and 36/90 = 2/5.
Why the other options are wrong
A (2/5): Leaves out the numbers ending in 0, counting 36 instead of 45.
B (9/20): Divides 45 by 100, as if there were 100 two-digit numbers.
D (5/9): Divides 45 by 81, leaving out numbers like 33 with equal digits, which can still be chosen.
How does your child work out a probability?
Count the outcomes you want, then put them over all the equally likely outcomes. A probability sits between 0 and 1, and it can be written as a fraction, a decimal or a percentage.
When something changes first, such as a lolly being eaten, the total changes too. Your child should update the counts before writing the fraction.
For harder questions, list outcomes in a system: by the first digit, by the first card, or in a grid. Counting in groups is faster than listing every case, and much less likely to miss one.
What traps should your child watch for?
Each slip below answers a slightly different question from the one asked. If your child's answer matches one, name the slip together and check the group and the total on the next few questions.
Using the old total. After a lolly is eaten there are fewer to choose from. A fraction over the original total looks right but answers a different question.
The whole group instead of part of it. "Of the students who did not choose canoeing" means the total is only those students.
The middle row instead of the middle person. In a frequency table, the middle value of the first column isn't necessarily the median.
Forgetting zero. A ones digit can be 0, as in 50 or 90. Leaving those numbers out shrinks the count.
How do data questions link to other skills?
Through fractions. Every probability is a fraction, and every "what percentage" question is a fraction turned into a percentage, so the fractions page supports this one. Counting outcomes uses the same careful listing as number questions.
Collect small sets of real data: bedtimes in the family, goals across a season, the top temperature each day for a week. Ask your child for the mean, the median and the range, and which gives the fairest picture.
Board games with dice are good for chance. Before a roll, ask how likely a total is, then list the outcomes to check.
In the app, the data lesson has an Interactive version and Notes. There are also drills by section and topic; a free account drills the free test's questions, and a paid plan opens the rest.
Four questions show the method; the Mathematics section of Practice test 1 shows whether your child can use it against the clock. Afterwards, results by skill separate data and chance from the rest of Mathematics.
