Descriptive statistics is often distinguished from purely mathematical statistics, or statistical inference. With descriptive statistics you know all data in question and you want to summarize it: you have to know all purchases made in a store (your accounting system keeps them all), all your students' quiz results, etc. With inferential statistics, you try to estimate what the whole dataset looks like based on a sample.
Why would you work with a sample? First, it may be impossible to measure all items you're interested in. If you're working with a typical height of men in your country, there are thousands or millions of men in the population, and measuring them all is not feasible. Another reason is that measuring could potentially destroy an item. For example you may be interested in the lifespan of light bulbs. However, you can only measure the lifespan of a light bulb after it has stopped working. If you work for a light bulb factory, you don't want to deplete all your products just to measure their lifespan! Therefore, you have to measure only a sample of light bulbs and estimate measurments for the batch based on the sample.
Inferential statistics talks to you in descriptive statistics' terms. Inferential statistics provides you with estimates for descriptive statistics for the whole population. In other words, you need to know and understand descriptive statistics in order to understand what the population looks like based on the estimates provided by inferential statistics.
Real world scenarios:
- You work for a men's clothing company. You have to decide how many suits in each size you're going to make, so you need to know the common heights of men in your country. You cannot measure all men in your country, but you can gather 100 (or 1000) men sample, measure them and use inferential statistics to estimate what the whole population looks like.
- You distribute a customer survey. Of course, not all customers will answer the survey. Inferential statistics helps you to transfer results of the survey to all your customers.