Question

which table shows negative correlation?

x	y
2	12
3	10
4	17
5	18
x	y
1	25
2	23
3	15
4	17
5	12
x	y
1	28
2	20
3	24
4	22
5	23

Explanation:

Step1: Recall negative - correlation concept

In a negative - correlation, as the value of $x$ increases, the value of $y$ generally decreases.

Step2: Analyze the first table

For the first table: when $x$ increases from 1 to 2, $y$ decreases from 19 to 12; but when $x$ increases from 3 to 4, $y$ increases from 10 to 17, so it does not show a consistent negative correlation.

Step3: Analyze the second table

For the second table: as $x$ increases from 1 to 2, $y$ decreases from 25 to 23; as $x$ increases from 2 to 3, $y$ decreases from 23 to 15; as $x$ increases from 3 to 4, $y$ decreases from 15 to 17 (a small non - decreasing value but overall trend is decreasing); as $x$ increases from 4 to 5, $y$ decreases from 17 to 12. It shows a general trend of $y$ decreasing as $x$ increases.

Step4: Analyze the third table

For the third table: when $x$ increases from 1 to 2, $y$ decreases from 28 to 20; but when $x$ increases from 2 to 3, $y$ increases from 20 to 24, so it does not show a consistent negative correlation.

Answer:

The second table shows negative correlation.