This is part of our collection of Short Problems.
You may also be interested in our longer problems on Statistics - Stage 4.
Printable worksheets containing selections of these problems are available here
problem
Average discovery
Age
14 to 16
Challenge level
Find the missing number if the mean, median and mode are all the same.
problem
Partial means
Age
14 to 16
Challenge level
From the mean of 64 numbers, and the mean of the first 36 of these numbers, can you work out the mean of the last 28 numbers?
problem
Ladybird football team
Age
14 to 16
Challenge level
The ladybird squad members have an average of 12 spots each. How many spots does the pine ladybird have?
problem
Mean balance
Age
14 to 16
Challenge level
Given information about the mean, can you work out the missing numbers?
problem
Beta rovers
Age
14 to 16
Challenge level
Can you find the mode and median number of goals scored by Beta Rovers?
problem
Gamma city
Age
14 to 16
Challenge level
Can you find the mode and median number of goals scored by Gamma City?
problem
Algebraic average
Age
14 to 16
Challenge level
The mean of three numbers x, y and z is x. What is the mean of y and z?
problem
Dopey measurement
Age
14 to 16
Challenge level
How does Snow White need to change her result after the mix-up?
problem
Equal means
Age
14 to 16
Challenge level
What value of x makes the mean of the first three numbers in this list equal to the mean of the other four?
problem
Acceptance rate
Age
14 to 16
Challenge level
The mean number of students has changed, so how many students applied to a school?
problem
Mean median
Age
14 to 16
Challenge level
Can you work out the median weight of these children from the given means?
problem
Smallest range
Age
14 to 16
Challenge level
What is the smallest possible range that these 4 integers could have?
problem
Maximum mean
Age
14 to 16
Challenge level
What is the largest that the mean of these numbers could be?
problem
Driving test
Age
14 to 16
Challenge level
Which driving test centre has the highest pass rate?
problem
Prize pony
Age
14 to 16
Challenge level
When Helen moved her favourite pony from one stable to another, the average value of the horses in each stable increased by £10000. What is the total value of all the ponies?
problem
Possible range
Age
14 to 16
Challenge level
The median of a set of five positive integers is one more than the mode and one less than the mean. Can you find the largest range possible?
problem
Pay attention
Age
14 to 16
Challenge level
If some of the audience fell asleep for some of this talk, what was the average proportion of the talk that people heard?
problem
Changing averages
Age
14 to 16
Challenge level
Find the value of $m$ from these statements about a group of numbers
problem
Very average
Age
14 to 16
Challenge level
If each number in this list is the average of the two numbers before it, what is the value of a?