# Statistics Stage 4 - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Statistics - Stage 4.

### Algebraic Average

##### Age 14 to 16 Short Challenge Level:

The mean of three numbers x, y and z is x. What is the mean of y and z?

### Partial Means

##### Age 14 to 16 Short 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?

### Possible Range

##### Age 14 to 16 Short 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?

### Pay Attention

##### Age 14 to 16 Short 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?

### Changing Averages

##### Age 14 to 16 Short Challenge Level:

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

### Jewellery Boxes

##### Age 14 to 16 Short Challenge Level:

When a jewel worth £5000 is transferred from one box to another, the average value of the jewels in both boxes increases. What is the total value of all the jewels?

### Prize Pony

##### Age 14 to 16 Short 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?