Question

high winds make wildfires more dangerous. the table shows the number of days of high winds during a recent wildfire. (wind speed is measured in miles per hour, or mph.)
wildfire data
which scatterplot best represents the data?

Explanation:

Step1: Identify data points

We have data points \((x,y)\) where \(x\) is the number of days and \(y\) is the wind speed. The points are \((4,80)\), \((2,50)\), \((1,75)\), \((3,65)\), \((2,70)\), \((1,75)\), \((2,60)\), \((3,55)\)

Step2: Analyze scatter - plot features

• For \(x = 1\), \(y=75\) (two points).
• For \(x = 2\), \(y\) values are \(50\), \(70\), \(60\)
• For \(x = 3\), \(y\) values are \(65\), \(55\)
• For \(x = 4\), \(y = 80\)

Looking at the first scatter - plot:

• When \(x = 1\), the \(y\) - values (around \(70 - 80\)) match our data (\(y = 75\) twice).
• When \(x=2\), the \(y\) - values (around \(50 - 70\)) match (\(y = 50\), \(70\), \(60\))
• When \(x = 3\), the \(y\) - values (around \(50 - 70\)) match (\(y=65\), \(55\))
• When \(x = 4\), \(y = 80\) matches.

The second scatter - plot has incorrect \(y\) - values for \(x = 2\) (the \(y\) - values for \(x = 2\) in the data are \(50\), \(70\), \(60\) but the second plot has a point near \(y = 50\) and two points near \(y=60 - 70\) which is not an exact match in terms of distribution).

The third scatter - plot has incorrect \(y\) - values for \(x = 2\) (the \(y\) - values in the data for \(x = 2\) are \(50\), \(70\), \(60\) but the third plot has a point near \(y = 50\) and two points near \(y = 40 - 50\) which is wrong).

The fourth scatter - plot has \(y\) - axis range issues (the \(y\) - axis in the data has values up to \(80\) but the fourth plot's \(y\) - axis seems to have a maximum of around \(80\) but the distribution of points for each \(x\) is not correct, for example, for \(x = 2\) the points are too low).

Answer:

The first scatter - plot (the one with \(y\) - values ranging from \(10\) to \(90\) and \(x\) - values from \(0\) to \(4\) where the points are distributed as per the data \((4,80)\), \((2,50)\), \((1,75)\), \((3,65)\), \((2,70)\), \((1,75)\), \((2,60)\), \((3,55)\)) is the correct one.