Modelling with spreadsheets

Computer models of mathematical data, such as budgets, are usually done

using a spreadsheet application that processes and performs calculations

on the data entered by the user. For example, a computer model of a

school's budget might show that the school will run out of money before

the end of the term if it hires an extra teacher.

How spreadsheets work

A spreadsheet appears as a grid, each row has its own number and each column its

own letter. This labelling of rows and columns is used to give each cell a cell address

or reference, for example, C5 means column C, row 5.

It is also possible to refer to a range of cells collectively, ie E4:E12 includes E4, E12

and all of the cells in-between.

Cells can contain numbers, text or formulae.

Example spreadsheet

A grocer uses a mobile shop to sell groceries to customers who live out of town. He

uses a spreadsheet to keep a record of his daily sales:

Daily sales

A B C D E

3 Produce Unit Number sold Price Sales

4 Apples kg 7 £0.70 £4.90

5 Potatoes 25kg 8 £6.00 £48.00

6 Oranges kg 6 £0.90 £5.40

7 Carrots 25kg 8 £8.50 £68.00

8 Sprouts kg 4 £1.40 £5.60

9 Cabbage kg 6 £0.70 £4.20

10 Onions kg 9 £0.56 £5.04

11

12 Total £141.14

There are a number of formulae in the above spreadsheet but they're hidden; only

the results are displayed.

Formulae

The formula in cells E4 to E10 works out the total value of sales for each item. It does

this by multiplying the number sold by the individual price. For example, seven

kilograms of apples were sold at 70p per kilogram; the sales total is calculated as

£4.90 and is displayed in the cell E4. The formula in E4 is =C4*D4, i.e. 7 × £0.70.

Cell E12 contains a formula that calculates the total value of the sales column. The

formulae used is =SUM(E4:E10). This formula includes cells E4, E10 and all of the

cells in-between. You could write it =E4+E5+E6+E7+E8+E9+E10 which will give

the same result but is overly complex and leaves more room for mistakes. Note, the

=SUM function should only be used when adding a range of cells.

Constructing a spreadsheet

A self-employed builder charges £15.00 an hour. He's constructed a spreadsheet to

keep a record of his work but it's incomplete.

Complete the builder's spreadsheet

Document

Download the builder's incomplete spreadsheet.

Open the spreadsheet here

Download the incomplete spreadsheet on the left and perform the tasks below. To

open it you will need a spreadsheet application, eg Microsoft's Excel,

OpenOffice.org's Calc, Google Docs or another application that can open *.xls files.

Please note that the actual steps required to complete each tasks may differ slightly

depending on the spreadsheet application you're using.

Task 1

The builder has just completed some work for Jason Williams. It took him four

hours and the materials cost £37.00.

1. Enter Jason’s information into the spreadsheet.

The formulae to calculate the bill should be automatically inherited from the cell

above.

Task 2

Changing the category to currency

The values stored in columns C and D are currency. Change the number category to

currency so the spreadsheet recognises this.

1. Click cell C2 and hold down the left mouse button. Move the cursor across

to cell D2 and then down to cell D6. The cells should now be highlighted.

2. Release the left mouse button and right-click on a highlighted cell. Click

Format Cells.

3. A new screen appears, click the Number tab and click currency in the list.

4. Click OK.

Task 3

There’s a mistake in the formula used to calculate the total bill, the builder has

entered his hourly rate incorrectly – correct his mistake (remember, his hourly rate is

£15).

1. Double-click cell D2 to edit the formula. Make the correction and press

enter on the keyboard to save the changes.

2. Copy the changes to the formula to the cells below. Click cell D2, left-click

the small black square in the bottom right corner and drag it down to cell D6.

Release the left mouse button.

Task 4

You can select specific cells to use in your formula

The builder wants to calculate his daily earnings, write a formula in cell D8 to do this

for him. Press enter to save the changes.

The formula can be written two ways, decide which one to use:

1. =D2+D3+D4+D5+D6

2. =SUM(D2:D6)

The spreadsheet program should realise you’re adding together currency and

automatically change cell D8’s number category to match.

Document

Download the builder's completed spreadsheet.

Open the spreadsheet here

Download the completed spreadsheet on the left to see how you did or to learn

where you went wrong.

Advantages of using spreadsheets

Using a spreadsheet rather than a calculator or pen and paper offers the following

advantages:

More effective data handling

Formulae can be used to instantly recalculate totals. For example, if the

builder changed his call-out charge, the total cost would be instantly recalculated

taking the change into account.

You can carry out "what if?" investigations. For example, the grocer could

increase his prices to see the effect on sales and the builder could increase his

hourly charge to see the effect on his daily total.

The information can be presented in different ways. For example, the

grocer could produce a graph of fruit and vegetable sales by choosing the ranges

A4:A10 and E4:E10 in order to make the graph.

It is easy to make these changes, save your work and print it out again.

More flexible presentation

Alter column widths and easily delete or add columns and rows.

Underline, embolden text and use different fonts and graphics.

Justify your data to the left, centre or right.

Control the types of numbers you enter - for example you can choose

percentage, currency or set the number of decimal places.

Modelling: what if?

A spreadsheet can be used as a modelling tool.

The model is controlled by a set of rules introduced by formulae. These rules can be

changed easily to vary the model and, for example, provide information about

running costs and profit margins.

A company could use a spreadsheet to find out what would happen if they reduced

the price of their product, and the effect it would have on their income from sales. To

do this they lower the value in the price column and the data in the income from

sales column will be automatically recalculated (downwards). If the lower price

resulted in higher sales, by adjusting the data in the number of sales column, the

income from sales data will again be recalculated (upwards).

Being able to answer "what if?" questions like this is vital and allows a company to

predict future trends in its income and outgoings.

Why use computer models?

As well as financial modelling, spreadsheet software can be used for many other

kinds of computer model:

modelling supermarket queues

modelling the stresses which will be borne by a new bridge

modelling traffic flow in a new road system

Computer models are cheaper to setup than alternative methods that could be used

to predict what will happen in a system, eg building a prototype. Other benefits

include being able to:

make alterations and quickly see the outcomes

repeat tests several times over

learn from "what if?" scenarios

model dangerous situations safely

Limitations of computer models

A model is only as good as the rules used to create it. A mistake could have been

made by whoever wrote the model and not every situation might have been

considered – both of these issues could cause the model to give incorrect answers.

http://www.bbc.co.uk/schools/gcsebitesize/ict/modelling/0spreadsheetsrev1.shtml