Statistics Short Problems - Age 11-14


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:

Stage 3 ★ Sheet 1 Solutions            Stage 3★★  Sheet 1 Solutions
  Sheet 2 Solutions                 


Average Discovery

Age 11 to 14 Short Challenge Level:

Find the missing number if the mean, median and mode are all the same.

Choose the Mean

Age 11 to 14 Short Challenge Level:

Find 4 numbers which have a mean of 7, a median of 8 and a mode of 9.

Ice Cream Pie

Age 11 to 14 Short Challenge Level:

The pie chart shows the different types of ice creams on sale. How many chocolate ice creams were sold?

Median Matches

Age 11 to 14 Short Challenge Level:

Can you find the mode and median from bar and pie charts?

Kate's Date

Age 11 to 14 Short 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?

Mean Balance

Age 11 to 14 Short Challenge Level:

Given information about the mean, can you work out the missing numbers?

Rugby and Ballet

Age 11 to 14 Short Challenge Level:

What is the average weight of five ballet dancers and ten rugby players?

Balancing the Books

Age 11 to 14 Short Challenge Level:

How many visitors does a tourist attraction need next week in order to break even?

Sevens

Age 11 to 14 Short Challenge Level:

What is the largest number Sophie can use to have seven positive integers with a mean of 7?

Ladybird Football Team

Age 11 to 14 Short Challenge Level:

The ladybird squad members have an average of 12 spots each. How many spots does the pine ladybird have?

Range of Averages

Age 11 to 14 Short Challenge Level:

Find these 4 numbers, given their mode, median and range.

Bat Wings

Age 11 to 14 Short Challenge Level:

Two students collected some data on the wingspan of bats, but each lost a measurement. Can you find the missing information?

Acceptance Rate

Age 11 to 14 Short Challenge Level:

The mean number of students has changed, so how many students applied to a school?

Rendezvous

Age 11 to 14 Short Challenge Level:

In which town should five friends meet, in order to keep the total travelling distance as small as possible?

Average Temperature

Age 11 to 14 Short Challenge Level:

The average temperature of six cities is 5$^\circ$C. What is the average temperature when two cities are added?

Mean Median

Age 11 to 14 Short Challenge Level:

Can you work out the median weight of these children from the given means?

Dopey Measurement

Age 11 to 14 Short Challenge Level:

How does Snow White need to change her result after the mix-up?

Shifting Average

Age 11 to 14 Short Challenge Level:

What happens to the average if you subtract 8 from all of the numbers?

Any Means Possible

Age 11 to 14 Short 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?

French Test

Age 11 to 14 Short Challenge Level:

What was the average score in this French test?

Mean Square

Age 11 to 14 Short 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?

Number of Arms

Age 11 to 14 Short Challenge Level:

What is the probability that the next person you meet has an above average number of arms?

Grandpa's Rock Cakes

Age 11 to 14 Short 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?

A Mean Calculation

Age 11 to 14 Short Challenge Level:

What is the mean of this set of numbers?

The Mean Problem

Age 11 to 14 Short Challenge Level:

Can you work out the four unknown numbers from the clues about their means?

Committees

Age 11 to 14 Short Challenge Level:

Every member of the club is a member of two committees. How many members are there in the club?

Equal Means

Age 11 to 14 Short 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?

The Average Age

Age 11 to 14 Short Challenge Level:

Given this information about averages, find the ages of these teachers.

Maximum Mean

Age 14 to 16 Short Challenge Level:

What is the largest that the mean of these numbers could be?