Given:
- r = 0.25 (correlation coefficient)
- E(x-x)(y-y) = 60 (sum of cross-products of deviations)
- E(x-x)^2 = 90 (sum of squared deviations of x)
- SDof Y = 4 (standard deviation of variable Y)

To Find:
The number of pairs of observations from the given data.

Solution:

To find the number of pairs of observations, we need to use the formula for the correlation coefficient (r):

r = (E(x-x)(y-y)) / sqrt(E(x-x)^2 * E(y-y)^2)

Given that r = 0.25, we can rearrange the formula to solve for sqrt(E(x-x)^2 * E(y-y)^2):

0.25 = 60 / sqrt(90 * E(y-y)^2)

Squaring both sides of the equation, we get:

0.0625 = (60^2) / (90 * E(y-y)^2)

Simplifying further:

0.0625 = 3600 / (90 * E(y-y)^2)

Cross-multiplying:

(90 * E(y-y)^2) * 0.0625 = 3600

Dividing both sides by 0.0625:

90 * E(y-y)^2 = 3600 / 0.0625

Simplifying further:

90 * E(y-y)^2 = 57600

Dividing both sides by 90:

E(y-y)^2 = 57600 / 90

Now, we need to use the formula for the standard deviation (SD) to find the sum of squared deviations of y:

SD^2 = E(y-y)^2 / n

Given that SDof Y = 4, we can rearrange the formula to solve for E(y-y)^2:

4^2 = E(y-y)^2 / n

16 = E(y-y)^2 / n

Cross-multiplying:

E(y-y)^2 = 16n

Substituting the value of E(y-y)^2 from the previous calculation:

57600 / 90 = 16n

Simplifying further:

640 = 16n

Dividing both sides by 16:

n = 40

Therefore, the number of pairs of observations is 40.