**Rank Correlation Coefficient**

The rank correlation coefficient measures the strength and direction of the relationship between two sets of rankings. It is used to determine the similarity or dissimilarity of the orderings of two variables.

**Given Information**

In this case, we are given that there are 8 students and their ranks for mathematics and statistics marks. We are also given that the sum of squares of differences in ranks is 50.

**Finding the Rank Correlation Coefficient**

To find the value of the rank correlation coefficient, we can use the formula:

ρ = 1 - (6Σd²)/(n(n²-1))

where:
- ρ is the rank correlation coefficient
- Σd² is the sum of squares of differences in ranks
- n is the number of observations (in this case, the number of students)

**Step 1: Calculate the Sum of Squares of Differences in Ranks**

Given that the sum of squares of differences in ranks is 50, we can substitute this value into the formula:

50 = Σd²

**Step 2: Calculate the Rank Correlation Coefficient**

Now, we can substitute the known values into the formula and calculate the rank correlation coefficient:

ρ = 1 - (6*50)/(8*(8²-1))

Simplifying this equation:

ρ = 1 - (300)/(8*(64-1))
= 1 - (300)/(8*(63))
= 1 - 300/504
= 1 - 0.5952
= 0.4048

Therefore, the value of the rank correlation coefficient is 0.4048.

**Explanation**

The rank correlation coefficient ranges from -1 to +1. A positive value indicates a positive correlation, meaning that as one variable increases, the other variable tends to increase as well. A negative value indicates a negative correlation, meaning that as one variable increases, the other variable tends to decrease.

In this case, since the rank correlation coefficient is positive (0.4048), it suggests a weak positive correlation between the ranks of mathematics and statistics marks. This means that as the rank of a student's mathematics mark increases, their rank in statistics marks tends to increase as well, although not very strongly.

It is important to note that the rank correlation coefficient only measures the strength and direction of the relationship between the ranks, not the actual values of the variables themselves.

1-[(6×50)÷( 8^3 - 8)] = 1-[300÷ 504] = 1-0.6 = 0.4