This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

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### M, M and M

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

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### How would you score it?

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

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### Olympic Records

Can you deduce which Olympic athletics events are represented by the graphs?

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### Statistical shorts

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

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### About Average

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

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### Half a minute

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

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### Substitution Cipher

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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### In the bag

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

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### Reaction timer

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

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### 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?

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Favourite

### What's the weather like?

With access to weather station data, what interesting questions can you investigate?

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### Estimating time

How well can you estimate 10 seconds? Investigate with our timing tool.

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### Wipeout

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

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### Unequal Averages

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

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### 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...

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### Tree tops

Can you make sense of information about trees in order to maximise the profits of a forestry company?

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*ou may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.*