1.3.4: Calculating means using frequencies and calculating weighted means

In some situations, various values in the batch get repeated (there may be a limited number of different values that can occur, for example). It can be simpler to group the data and record the number of times with which each different value occurs. The number is called the *frequency*. The following example explores this possibility and comes up with an equivalent formula for calculating the mean of the batch.

1.4 Converting ratios from fractions to decimals

Although ratios are often given as fractions, they can also be expressed as decimals. You need to deal with a mixture of fractions and decimals, and to compare ratios given in either form, so you need to be able to convert between the two forms.

## Example 4

The ratio of the circumference of a cir

Time conversions are also ratios. The ratio of time measured in minutes to time measured in seconds is one to sixty (1:60), as there are sixty seconds in a minute.

## Example 2

Adam's grandfather ran a mile in Author(s):

**1** A friend is painting the inside walls of a garage. So far she has used a 2 litre tin of emulsion paint and covered an area of 9 m^{2}. She needs some more paint. How much more would you advise her to purchase if she intends to pa

To make short crust pastry, one recipe book says â€˜use one part of fat to two parts of flourâ€™; another recipe says â€˜use fat and flour in the ratio of one to twoâ€™; and yet another says â€˜use half as much fat as flourâ€™. These are different ways of expressing the same ratio. Ratios are often expressed as fractions. So in this case:

2.3 Paper-and-glue constructions

In this section we show how to construct surfaces by taking a piece of paper in the shape of a polygon and gluing some of its edges together. The surfaces that we obtain occupy a central position in this unit, as you will see.