If a set of xy-axes has 20 grid units in each direction and the greatest value the data to be placed on the horizontal axis is 132, what would be the appropriate and convenient scale to use for this axis? explain

Given that the xy-axis has 20 grid units in each direction and the greatest value the data to be placed on the horizontal axis is 132, then the appropriate and convenient scale to use for the horizontal axis is 1 to 8.

Thus will make the graph spread adequately across the axis as well provide a good sub-units for the graph (i.e. each grid unit will be divided into 8 equal subunits)

In general, you want the graph to occupy as much room as possible. This makes interpolation of values on the graph easier to perform. And since you have 20 units, the largest possible value would be 132 / 20 = 6.6. However, you also want the units to be easy to handle while counting and 6.6 is rather messy. So you increase to the next larger integer which would be 7. And 7 would work, but it's still rather hard to handle. For instance, what's 13 multiplied by 7? That's not something most people do easily, so you'll want to round up to a power of 2, 5, or 10 for the greatest ease of use. That leaves as reasonable candidates the numbers 8, or 10. So for that axis, there are three choices with advantages and disadvantages. 7 - Gives the largest graph for more detail, but an inconvenient scale to quickly multiply by. 8 - Almost as good as 7 for graph detail, but still a bothersome scale to multiply by. 10 - Not as good in terms of the graph size ( you'll only be using 14 of the 20 divisions). But it is a very convenient size to multiply by. Given the lack of detailed knowledge of the data this graph needs to display, I'd recommend using 10 units per division on the graph.