Question

a data set goes from 32 °f to 80 °f. there are 12 lines on the axis of the graph. how should the lines of the graph be labeled? every 3 °f every 5 °c every 4 °f

Explanation:

Step1: Calculate the range of the data set

The range \(R\) of the data set is \(R = 80 - 32=48^{\circ}F\).

Step2: Analyze the number of intervals

There are \(n = 12\) lines on the axis. But the number of intervals \(k\) between the lines is \(k=12 - 1=11\). Let the interval size be \(x\). We want to find a value \(x\) such that \(x\times k\approx R\).

• If \(x = 3^{\circ}F\), then \(3\times11 = 33

eq48\)

• If \(x = 4^{\circ}F\), then \(4\times11=44\)
• If \(x = 5^{\circ}C\), the unit is wrong as the data set is in \(^{\circ}F\)

Another way: We can also think about it as dividing the range into \(12\) - 1=11 parts. \(48\div11\approx4.36\). But if we consider the axis - labeling convention (usually we use a round - number interval that can cover the range). The range from \(32\) to \(80\) (a difference of \(48\)). If we use an interval of \(4^{\circ}F\):
Start at \(32\), then \(32 + 4=36\), \(36+4 = 40\), \(\cdots\), \(32+(11\times4)=32 + 44=76\) (and we can extend a bit to cover up to \(80\))

Answer:

Every \(4^{\circ}F\)