Question

which table shows a positive correlation?

Explanation:

Step1: Understand positive correlation

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

Step2: Analyze the first table

In the first table, \(x\) values are \(1,2,2,4,5\) and \(y = 5\) for all \(x\). \(y\) is constant as \(x\) changes. So no positive correlation.

Step3: Analyze the second table

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

Step4: Analyze the third table

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

Step5: Analyze the fourth table

In the fourth table, \(x = 8\) for all values and \(y\) changes. \(x\) is constant as \(y\) changes. So no positive correlation.

Answer:

The second table.