How to find the threshold for splitting Continuous valued features

Course Q&A Machine Learning Specialization Advanced Learning Algorithms
1

in the week4 Continuous valued features, andrew said "

In the more general case, we’ll actually try not just three values, but multiple values along the X axis. And one convention would be to sort all of the examples according to the weight or according to the value of this feature and take all the values that are mid points between the sorted list of training. Examples as the values for consideration for this threshold over here. This way, if you have 10 training examples, you will test nine different possible values for this threshold and then try to pick the one that gives you the highest information gain."

image
image1257×624 94.7 KB

I am not really getting what he is saying here, why the middle points of the sorting list has 9 values? isn’t the middle value of this sorting lit is around 9?

2

Say you have 10 points that form an irregular line. And you want to find the midpoint between each adjacent pair. You will have nine locations.