6 Making Predictions Using the Central Limit Theorem and SciPy

The Normal distribution is a bell-shaped curve that we introduced in Section Three. The curve arises naturally from random data sampling, due to the Central Limit Theorem. Previously, we noted how according to that theorem, repeatedly sampled frequencies will take the shape of a Normal curve. Furthermore, the theorem predicts a narrowing of that curve as the size of each frequency-sample goes up. In other words, the distribution’s standard deviation should decrease as the sampling size grows larger.

The Central Limit Theorem lies at the heart of all classic statistics. In this section, we probe the theorem in great detail, using the computational power of SciPy. Eventually, we will learn how to leverage the theorem to make predictions from limited data.

6.1 Manipulating the Normal Distribution Using SciPy

6.1.1 Comparing Two Sampled Normal Curves

6.2 Determining Mean and Variance of a Population through Random Sampling

6.2.1 Making Predictions Using Mean and Variance

6.3.1 Computing the Area Beneath a Normal Curve

6.3.2 Interpreting the Computed Probability

6.4 Summary