Recall that in the last exercise, we began investigating whether or not there is an association between math scores and the school a student attends. We can begin quantifying this association by using two common summary statistics, mean and median differences. To calculate the difference in mean G3 scores for the two schools, we can start by finding the mean math score for students at each school. We can then find the difference between them:

mean_GP = np.mean(scores_GP)
mean_MS = np.mean(scores_MS)
print(mean_GP) #output: 10.49
print(mean_MS) #output: 9.85
print(mean_GP - mean_MS) #Output: 0.64

We see that the mean math score for students at GP is 10.49, while the mean score for students at MS is 9.85. The mean difference is 0.64. We can follow a similar process to calculate a median difference:

median_GP = np.median(scores_GP)
median_MS = np.median(scores_MS)
print(median_GP) #Output: 11.0
print(median_MS) #Output: 10.0
print(median_GP-median_MS) #Output: 1.0

GP students also have a higher median score, by one point. Highly associated variables tend to have a large mean or median difference. Since “large” could have different meanings depending on the variable, we will go into more detail in the next exercise.