This book is in Open Review. I want your feedback to make the book better for you and other readers. To add your annotation, select some text and then click the on the pop-up menu. To see the annotations of others, click the button in the upper right hand corner of the page

Chapter 4 Population and sampling

Consider a case, when you want to understand what is the average height of teenagers living in your town. It is very expensive and time consuming to go from one house to another and ask every single teenager (if you find one), what their hight is. If we could do that, we would get the true mean, true average height of teenagers living in the town. But in reality, it is more practical to ask a sample of teenagers and make conclusions about the “population” (all teenagers in the town) based on this sample. Indeed, you will spend much less time collecting the information about the height of 100 people rather than 100,000. However, when we take a sample of something, the statistics we work with will always differ from the truth: sample mean will never be equal to the true mean, but it can be shown mathematically that it will converge to the truth, when some specific conditions are met and when the sample size increases. If we set up the experiment correctly, then we can expect our statistics to follow some laws. In this chapter, we discuss these laws, how they work and what they imply.