Using the data, let’s plot the Scatter diagram to see if there is any relationship between the Test score (or marks obtained) and the number of hours studied. Visually looking at this we can make a fair estimate that the test score improves with the number of hours studied.

The next step is to find out correlation coefficient (r) for the sample data we collected.

Here we had small sample data so are looking at the sample correlation coefficient. When you’re looking for the correlation coefficient for the whole population, which of course is not an easy thing, which is represented by row (ρ), instead of (r).

  • Correlation coefficient for sample data – r
  • Correlation coefficient for the population – ρ

The formula for the Correlation coefficient:

 

Or

Both of these basically mean the same thing you can pick any of these. I will be using the first one to do the calculation.

To calculate the value of r, I’ve put all these values in this formula. If you solve this using the calculator, you will find that the value of r to be 0.87935.

What does this value mean?

The correlation coefficient has to be something between -1 and +1.

  • +1.0 means the absolute relationship between two variables
  • Above 0.8 generally, means a strong relationship between two variables
  • Around 0.4 to 0.8 means that there is a medium relationship
  • Less than 0.4 means weak relationship

 

The sign of the r (plus or minus) tells us whether one variable increases or decreases with the other variable. Here in this case score increases with hours of study. So that’s the reason the value of r is positive.

Summary of the result

From the given data sample, we can conclude that there is a strong positive relationship between numbers of hours studied and the test score.