Answer:

Given:
- Correlation coefficient of concurrent deviation = -1
- Sum of number of positive product sign is 0

To find:
- Number of pairs

Solution:
- Let us assume that there are 'n' pairs of data
- Correlation coefficient of concurrent deviation = -1 indicates that the data is perfectly negatively correlated
- This means that as one variable increases, the other variable decreases in a perfectly linear manner
- Sum of number of positive product sign is 0 indicates that there are equal number of positive and negative product signs
- Product sign is positive when both the variables have the same direction of deviation from the mean, and negative when they have opposite directions of deviation from the mean
- Since the data is perfectly negatively correlated, the direction of deviation from the mean will always be opposite for the two variables
- This means that there will be equal number of positive and negative product signs, and their sum will always be 0
- Therefore, the number of pairs will be n/2
- For example, if there are 4 pairs of data, then there will be 2 positive and 2 negative product signs, and the sum will be 0
- Hence, the number of pairs is equal to half of the total number of data pairs

Therefore, the number of pairs is equal to half of the total number of data pairs.