Question

1. higher order thinking the table shows the number of painters and sculptors enrolled in seven art schools. jashar makes an incorrect scatter plot to represent the data.

enrollment
number of painters: 30, 43, 47, 30, 11, 48, 20
number of sculptors: 25, 33, 50, 27, 6, 58, 45
a. what error did jashar likely make?
b. explain the relationship between the number of painters and sculptors enrolled in the art schools.
c. reasoning jashar’s scatter plot shows two possible outliers. identify them and explain why they are outliers. mp.2

Explanation:

Part a

In a scatter - plot, the independent variable is usually on the \(x\) - axis and the dependent variable on the \(y\) - axis. Here, we assume that the number of sculptors (\(x\)) is the independent variable and the number of painters (\(y\)) is the dependent variable. Jashar likely swapped the axes. The \(x\) - axis should represent the number of sculptors and the \(y\) - axis should represent the number of painters.

Part b

As the number of sculptors increases, the number of painters also tends to increase. For example, when the number of sculptors goes from \(6\) to \(25\) to \(27\) to \(33\) to \(45\) to \(50\) to \(58\), the number of painters goes from \(11\) to \(30\) to \(30\) to \(43\) to \(45\) to \(47\) to \(58\). So, there is a positive correlation between the number of painters and sculptors enrolled in the art schools.

Part c

An outlier is a data point that is far from the general pattern of the data.

• The point \((6,11)\): If we consider the general trend of increasing values, this point has a very low number of both sculptors and painters compared to the other data points.
• The point \((58,50)\): If we look at the general trend, when the number of painters is around \(50\), the number of sculptors for most of the non - outlier data points is in the \(25 - 45\) range. Here, the number of sculptors (\(58\)) is relatively high compared to the other data points for a painter count of around \(50\)

Answer:

a. Jashar likely swapped the \(x\) and \(y\) axes.
b. There is a positive correlation between the number of painters and sculptors.
c. The outliers are \((6,11)\) (has very low values compared to the trend) and \((58,50)\) (the \(x\) - value (number of sculptors) is much higher than what would be expected for a \(y\) - value (number of painters) of \(50\) based on the general trend of the non - outlier data points).