Question

This data is going to be plotted on a scatter graph.

Height (mm) - 45 3 65 28
Mass (g) - 17 9 26 33

The grid is shown below. Work out the values of A and B that would give the best scales if:
a) Height is plotted on the horizontal axis and Mass on the vertical axis.
b) Mass is plotted on the horizontal axis and Height on the vertical.

Answer 1

Answer:a) Height on the horizontal axis and Mass on the vertical axis:

A ≈ 2.58

b) Mass on the horizontal axis and Height on the vertical axis:

A ≈ 0.39

Explanation:

To determine the values of A and B that would give the best scales for the given data, we need to consider two scenarios:

a) Height on the horizontal axis and Mass on the vertical axis:

In this scenario, A represents the scale factor for the height, and B represents the scale factor for the mass. To find the best scales, we want to ensure that the data points are adequately spread out on the graph.

The height values are: 45, 3, 65, 28.

The mass values are: 17, 9, 26, 33.

To determine the scale factors, we need to find the ratio of the range of the height values to the range of the mass values:

Range of heights = maximum height - minimum height = 65 - 3 = 62

Range of masses = maximum mass - minimum mass = 33 - 9 = 24

The scale factor for the height, A, is given by:

A = Range of heights / Range of masses = 62 / 24 = 2.58 (approximately)

So, for the best scales when height is on the horizontal axis and mass on the vertical axis, A ≈ 2.58.

b) Mass on the horizontal axis and Height on the vertical axis:

Similarly, in this scenario, A represents the scale factor for the mass, and B represents the scale factor for the height.

The mass values are: 17, 9, 26, 33.

The height values are: 45, 3, 65, 28.

We calculate the range of the mass values and the range of the height values:

Range of masses = maximum mass - minimum mass = 33 - 9 = 24

Range of heights = maximum height - minimum height = 65 - 3 = 62

The scale factor for the mass, A, is given by:

A = Range of masses / Range of heights = 24 / 62 = 0.39 (approximately)

So, for the best scales when mass is on the horizontal axis and height on the vertical axis, A ≈ 0.39.

Answer 2

For height on the horizontal axis and mass on the vertical axis, the scale can be 0 to 70 with intervals of 10 mm for height and 0 to 40 with intervals of 5 g for mass. For mass on the horizontal axis and height on the vertical axis, the scale can be 0 to 40 with intervals of 5 g for mass and 0 to 70 with intervals of 10 mm for height.

To determine the best scales for the scatter graph, we need to find the range of values for both height and mass.

a) If height is plotted on the horizontal axis, we can observe that the heights range from 3 mm to 65 mm. Therefore, we can use a scale that goes from 0 to 70, with each interval representing 10 mm.

If mass is plotted on the vertical axis, the masses range from 9 g to 33 g. We can use a scale that goes from 0 to 40, with each interval representing 5 g.

b) If mass is plotted on the horizontal axis, the masses range from 9 g to 33 g. We can use a scale that goes from 0 to 40, with each interval representing 5 g.

If height is plotted on the vertical axis, the heights range from 3 mm to 65 mm. Therefore, we can use a scale that goes from 0 to 70, with each interval representing 10 mm.