Which table shows a positive correlation?
| x | y |
|---|---|
| 1 | 5 |
| 2 | 5 |
| 2 | 5 |
| 4 | 5 |
| 5 | 5 |
| x | y |
|---|---|
| 1 | 10 |
| 2 | 18 |
| 3 | 31 |
| 4 | 37 |
| 5 | 52 |
| x | y |
|---|---|
| 1 | 24 |
| 2 | 15 |
| 3 | 13 |
| 4 | 9 |
| 5 | 6 |
| x | y |
|---|---|
| 8 | 9 |
| 8 | 12 |
| 8 | 17 |
| 8 | 21 |
| 8 | 22 |
Answer (2)
Table 1: No correlation.
Table 2: Positive correlation.
Table 3: Negative correlation.
Table 4: No correlation.
Table 2 shows a positive correlation because as x increases, y increases. Table 2
Explanation
Analyzing the Problem We are given four tables of x and y values and asked to identify which table shows a positive correlation. A positive correlation means that as x increases, y also tends to increase. We will examine each table to determine the relationship between x and y .
Analyzing Table 1 Table 1: As x increases (1, 2, 2, 4, 5), y remains constant at 5. This indicates no correlation.
Analyzing Table 2 Table 2: As x increases (1, 2, 3, 4, 5), y increases (10, 18, 31, 37, 52). This indicates a positive correlation.
Analyzing Table 3 Table 3: As x increases (1, 2, 3, 4, 5), y decreases (24, 15, 13, 9, 6). This indicates a negative correlation.
Analyzing Table 4 Table 4: x remains constant at 8, while y increases (9, 12, 17, 21, 22). This indicates no correlation between x and y since x does not change.
Conclusion Based on our analysis, Table 2 shows a positive correlation because as x increases, y also increases.
Examples
Understanding correlations is useful in many real-world scenarios. For example, consider the relationship between the number of hours studied and exam scores. Generally, as the number of hours studied increases, the exam scores also tend to increase, showing a positive correlation. Similarly, in economics, there might be a positive correlation between advertising expenditure and sales revenue. Recognizing these relationships helps in making informed decisions and predictions.
Table 2 shows a positive correlation because as x increases, y also increases. The other tables do not show this trend. Thus, the correct answer is Table 2.
;
