3.7 Extract meaningful information from data  (Page 2/5)

1.1 As you can see in the graph, the horizontal axis is marked in years. The bars show the amount of money paid in instalments by James, or saved up for a car by Gabriel. You will notice that the light bar is always higher than the dark bar for a specific year. Does the light bar show Gabriel’s or James’s situation?

1.2 Can one say whether Gabriel or James acted most wisely?

1.3 If both friends earn the same amount every month and get regular salary increases every year, who has the most left over every month to spend on other necessities, and fun?

1.4 Use the values in the table and calculate how much money each young man used in total in purchasing his cars over the whole period from 2000 to 2013.

1.5 When your father offers you his old car (which is still in sound working order) as a gift when you start work, will you accept and start saving for a new car of your own in a few years (like Gabriel) or will you decline his offer and buy a new car on hire purchase like James? Explain your answer.

1.6 Speak to a car salesman who sells new cars and ask him / her to explain exactly which conditions you have to comply with before you can enter into a hire purchase agreement. Ask about insurance, about who owns the car and about what happens if you can’t continue with your repayments.

2 Straight-line graphs with positive gradients show a direct relationship between two variables. Some graphs show an inverse relationship between two variables. We will look at two situations with this kind of relationship.

2.1 Here is a situation that we will return to in the section on probability:

You have to guess a number between 1 and 6. A friend rolls one dice. You have one chance out of 6 of being right.

If your friend rolls two dice (plural of die) and you guess one number, you have six chances out of 21 of being right. If you guess two numbers, then there is only one chance out of 21 of getting both numbers right.

With three dice, guessing one number gives you a chance of 21 out of 56; two numbers gives 6 out of 56 and guessing all three numbers gives a chance of one out of 56.

Here is the scatter plot for the three-dice game, and one for a four-dice game.

If you can imagine a curved line in each graph going through the points (it isn’t sen­sible to join the points – why?), you will notice the lines have the same general shape. This shape of graph illustrates an inverse relationship between two variables.

2.2 Here is another practical example of this shape of graph:

Sindiswa and Alan are in charge of arranging a dance to raise money in support of the AIDS organisation in their neighbourhood. They can get a DJ who will do it for free, but they have to pay to hire a hall. There are four halls to choose from: A, costing R1 000 and accommodating 200; B, costing R1 400, accommodating 350; C, costing R1 800, accommodating 600 and D, costing R2 100 and accommodating 500.

They have drawn this graph showing how the four halls differ as far as costs go. Depending on how many people attend the dance (shown on the horizontal axis), the cost per person to cover the cost of the hall, is shown on the vertical axis. They would like to donate at least R4 000 to the charity, but it would be nice if they could make it R5 000.