Question

(score for question 3: ___ of 2 points)

1. a family is tracking its spending habits. over the past year, the grocery bill has ranged from $110 to $170. suppose you were going to plot these points on a coordinate grid.

(a) what is a good scale to use for the y - axis? explain your reasoning.
(b) what is a good interval to use for the y - axis? explain your reasoning.
answer:

Explanation:

Part (a)

Step1: Determine the range

The range of grocery bill is \(170 - 110=60\).

Step2: Consider a scale

A good scale for the \(y -\)axis (since the values are in dollars) could be \(1\) unit \( = 10\) dollars. The range \(60\) can be accommodated within a reasonable number of units (\(60\div10 = 6\) units above the starting point). Also, the values \(110,120,\cdots,170\) are multiples of \(10\), so it will make the plotting and reading of the graph easy.

Part (b)

Step1: Analyze the scale

If the scale is \(1\) unit \(=10\) dollars (from part (a)), a good interval is \(10\).

Step2: Justify the interval

Since the data points (\(110,120,\cdots,170\)) are spaced \(10\) apart. An interval of \(10\) will ensure that each data - point falls on a grid line. For example, if we start the \(y -\)axis at \(100\), then \(110\) is \(10\) units above \(100\), \(120\) is \(20\) units above \(100\) and so on.

Answer:

(a) A good scale for the \(y -\)axis is \(1\) unit \( = 10\) dollars. The range of the data (\(170 - 110=60\)) can be easily accommodated with this scale and the data values are multiples of \(10\).
(b) A good interval for the \(y -\)axis is \(10\). The data points (\(110,120,\cdots,170\)) are spaced \(10\) apart, so an interval of \(10\) ensures each data - point lies on a grid line.