Statistics & data: 11 Plus maths practice

Mean, median, mode, range and reading charts.

CoreIn almost every paper that tests this subjectAbout 60 seconds a question in the test

The big idea

Mean = total ÷ how many. Median = the middle value when in order. Mode = the most common. Range = largest − smallest.

When reading charts, check the scale on the axis carefully. Each gridline may be worth 2, 5 or 10.

Tips that save marks

  • Put numbers in order before finding the median.
  • If you know the mean and how many values, you can find the total.
  • Range is a single number, not “3 to 9”.

Now try five

Try each one before you look at the answer: answering from memory is what makes it stick. Tap an option to check it. Most children get three or four right at first; five out of five means move on to the next topic.

Question 1Aim for about 60 seconds

120 children were asked about their favourite sport. How many chose Swimming?

90°90°120°60°NetballSwimmingCricketGymnasticsFavourite sport
Show the worked answer

Answer: A, 30

How to work it out

Swimming has 90° of the 360° circle, which is 14. 14 of 120 = 30.

Why the other options are wrong

  • B (31): A near miss: check the working again.
  • C (1): Divide the angle by 360, not by the number of children.
  • D (90): This is the angle of the slice, not the number of children.
  • E (40): This is the number who chose Cricket.
Question 2Aim for about 60 seconds

What is the range of these numbers?

17, 21, 25, 23, 29

Show the worked answer

Answer: E, 12

How to work it out

Range = largest − smallest = 29 − 17 = 12.

Question 3Aim for about 60 seconds

What is the mean of these numbers?

38, 41, 45, 26, 44, 46

Show the worked answer

Answer: D, 40

How to work it out

  1. Add them: 240.
  2. Divide by how many there are (6): 40.
Question 4Aim for about 60 seconds

Between which two times did the temperature rise the most?

0246810121416182022248 am10 am12 pm2 pm4 pm6 pmTime of dayTemperature (°C)
Show the worked answer

Answer: C, 10 am and 12 pm

How to work it out

  1. Look for the steepest upward part of the line.
  2. From 10 am and 12 pm it rose from 13°C to 17°C, a rise of 4 degrees, the biggest rise.

Why the other options are wrong

  • A (8 am and 10 am): It rose by 2 degrees here, less than 4.
  • B (4 pm and 6 pm): The temperature fell between these times.
  • D (2 pm and 4 pm): The temperature fell between these times.
  • E (12 pm and 2 pm): It rose by 2 degrees here, less than 4.
Question 5Aim for about 60 seconds

120 children were asked about their favourite sport. How many chose Tennis?

150°90°60°60°NetballTennisGymnasticsFootballFavourite sport
Show the worked answer

Answer: C, 30

How to work it out

Tennis has 90° of the 360° circle, which is 14. 14 of 120 = 30.

Why the other options are wrong

  • A (90): This is the angle of the slice, not the number of children.
  • B (20): This is the number who chose Gymnastics.
  • D (31): A near miss: check the working again.
  • E (1): Divide the angle by 360, not by the number of children.

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