This is part of our collection of Short Problems.
You may also be interested in our longer problems on Statistics - Stage 3.
Printable worksheets containing selections of these problems are available here
problem
Choose the mean
Age
11 to 14
Challenge level
Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.
problem
Range of averages
Age
11 to 14
Challenge level
Find these 4 numbers, given their mode, median and range.
problem
Ice Cream Pie
Age
11 to 14
Challenge level
The pie chart shows the different types of ice creams on sale. How many chocolate ice creams were sold?
problem
Kate's Date
Age
11 to 14
Challenge level
When Kate ate a giant date, the average weight of the dates decreased. What was the weight of the date that Kate ate?
problem
Balancing the Books
Age
11 to 14
Challenge level
How many visitors does a tourist attraction need next week in order to break even?
problem
Rugby and Ballet
Age
11 to 14
Challenge level
What is the average weight of five ballet dancers and ten rugby players?
problem
Average temperature
Age
11 to 14
Challenge level
The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?
problem
Shifting Average
Age
11 to 14
Challenge level
What happens to the average if you subtract 8 from all of the numbers?
problem
The average age
Age
11 to 14
Challenge level
Given this information about averages, find the ages of these teachers.
problem
Alpha United
Age
11 to 14
Challenge level
Can you find the mode and median number of goals scored by Alpha United?
problem
Bat Wings
Age
11 to 14
Challenge level
Two students collected some data on the wingspan of bats, but each lost a measurement. Can you find the missing information?
problem
The Mean Problem
Age
11 to 14
Challenge level
Can you work out the four unknown numbers from the clues about their means?
problem
Rendezvous
Age
11 to 14
Challenge level
In which town should five friends meet, in order to keep the total travelling distance as small as possible?
problem
Sevens
Age
11 to 14
Challenge level
What is the largest number Sophie can use to have seven positive integers with a mean of 7?
problem
Mean Square
Age
11 to 14
Challenge level
Can you fill this square so that the number in the middle of each line is the mean of the two numbers on either side of it?
problem
Number of arms
Age
11 to 14
Challenge level
What is the probability that the next person you meet has an above average number of arms?
problem
Growing families
Age
11 to 14
Challenge level
What do these statistics about family size mean?
problem
Any Means Possible
Age
11 to 14
Challenge level
Can you find a way to break one of these rods so that one of the pieces is equal to the mean of the other two?
problem
Grandpa's Rock Cakes
Age
11 to 14
Challenge level
Grandpa made a super-heavy rock cake. Five people have guessed the weight of the cake. Can you work out the weight of his cake?
problem
Committees
Age
11 to 14
Challenge level
Every member of the club is a member of two committees. How many members are there in the club?