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There are **28** NRICH Mathematical resources connected to **Averages**, you may find related items under Handling, processing and representing data.

Problem
Primary curriculum
Secondary curriculum
### Unequal Averages

Play around with sets of five numbers and see what you can discover about different types of average...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Half a Minute

Anna, Ben and Charlie have been estimating 30 seconds. Who is the best?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Wipeout

Can you do a little mathematical detective work to figure out which number has been wiped out?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### About Average

Can you find sets of numbers which satisfy each of our mean, median, mode and range conditions?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Statistical Shorts

Can you decide whether these short statistical statements are always, sometimes or never true?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Would You Score It?

Invent a scoring system for a 'guess the weight' competition.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### For Richer for Poorer

Charlie has moved between countries and the average income of both has increased. How can this be so?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Searching for Mean(ing)

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### M, M and M

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stats Statements

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Match the Matches

Decide which charts and graphs represent the number of goals two football teams scored in fifteen matches.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Litov's Mean Value Theorem

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maximum Mean

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

Age 14 to 16

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### The Average Age

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

Age 11 to 14

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Range of Averages

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

Age 11 to 14

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Number of Arms

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

Age 11 to 14

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Changing Averages

Find the value of $m$ from these statements about a group of numbers

Age 14 to 16

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Shifting Average

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

Age 11 to 14

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Average Temperature

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

Age 11 to 14

ShortChallenge Level

Article
Primary curriculum
Secondary curriculum
### May the Best Person Win

How can people be divided into groups fairly for events in the Paralympics, for school sports days, or for subject sets?

Age 5 to 16

Problem
Primary curriculum
Secondary curriculum
### Top Marks

Can you make all of these statements about averages true at the same time?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### PDF

Given a probability density function find the mean, median and mode of the distribution.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Spread

Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mediant Madness

Kyle and his teacher disagree about his test score - who is right?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bat Wings

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

Age 11 to 14

ShortChallenge Level