Year 8 Interactive Maths - Second Edition

## Problem Solving Unit

### Problem 17.1  The Mean

The mean of a group of 5 numbers is 7.  What might the numbers be?

### Problem 17.2   The Median

The median of a group of 7 numbers is 10.  What might the numbers be?

### Problem 17.3   The Mean and Median

Describe a sample for which the median is 3 more than the mean.

### Problem 17.4  Mean is Equal to the Median

Five students sat for a mathematics test and four of those students received marks of 5, 6, 8 and 9 respectively.  Try to work out the score of the fifth student if the mean mark is equal to the median mark.

### Problem 17.5  The Score

Five students sat for a geography test and four of those students received marks of 5, 6, 8 and 8.  Try to work out the score of the fifth student if:
a.  the mean is equal to the mode.
b.  the mean is greater than the median.
c.  the mean is greater than 8.

### Problem 17.6  Adding a Number to Each Score

Find the effect on the mean when a set of scores has 4 added to each score.

### Problem 17.7  Each Score Doubled

Find the effect on the mean when a set of scores has each score doubled.

### Problem 17.8  Each Score Halved

Find the effect on the mean when a set of scores has each score halved.

### Problem 17.9   Percentage Increase

Find the effect on the mean when a set of scores has each score increased by 20%.

### Problem 17.10  Effect on the Median and Mode

Find the effect on:
i.  the median
ii.  the mode

when a set of scores has:
a.  5 added to each score
b.  each score doubled
c.  each score halved
d.  each score increased by 50%