Question

comparing tables of data
which table shows a positive correlation?

Explanation:

Step1: Understand positive correlation

Positive correlation means as \(x\) increases, \(y\) also increases.

Step2: Analyze first table

In the first table, \(x\) increases (\(1,2,2,4,5\)) but \(y = 5\) remains constant. So no positive correlation.

Step3: Analyze second table

When \(x = 1,y = 10\); \(x=2,y = 18\); \(x = 3,y=31\); \(x = 4,y = 37\); \(x=5,y = 52\). As \(x\) increases (\(1\to2\to3\to4\to5\)), \(y\) increases (\(10\to18\to31\to37\to52\)).

Step4: Analyze third table

When \(x = 1,y = 24\); \(x=2,y = 15\); \(x = 3,y=13\); \(x = 4,y = 9\); \(x=5,y = 6\). As \(x\) increases, \(y\) decreases. So no positive correlation.

Step5: Analyze fourth table

\(x = 8\) (repeated multiple times) and \(y\) has values \(9,12,17,21,22\). Since \(x\) is not consistently increasing (it's mostly \(8\)), it does not show a proper positive - correlation pattern where \(x\) increases and \(y\) increases.

Answer:

The second table.