Why We Sample: You Cannot Measure EveryoneSuppose you want the average height of every 16-year-old in your country.There are hundreds of thousands of them, spread everywhere, and new ones turn 16 every day.Measuring all of them is impossible: too many people, too much time, too much money.So instead you measure a smaller group and use it to estimate the whole.The whole of statistics starts here, learning about a huge group from a small slice of it.AnalogyTo check if a pot of soup is salty, you do not drink the whole pot.You stir it, then taste one spoonful, that spoonful is your sample.The stir is what makes the spoonful represent the whole pot, and that stir is what this whole subtopic is really about.Population Vs SampleA population is the entire group you want a conclusion about.In the height example the population is every 16-year-old in the country.A sample is the smaller part of the population that you actually collect data from.A sample of 200 students picked to represent all 16-year-olds is one example.We sample because measuring the whole population is often impossible, too slow, or too expensive.Sometimes measuring destroys the item, so you physically cannot test everything.ExampleA factory cannot crash-test every car it builds, so it tests a sample.NoteExam convention: at SL a given data set is treated as the population unless the question says otherwise.So calculations like the mean are population values, not sample estimates, unless told.Random Samples And Why Randomness MattersA random sample is one where every member of the population has an equal chance of being chosen.Crucially, whether someone is picked does not depend on their data value.The danger we are fighting is selection bias, where the way you choose systematically favours certain values.If you only measure the school basketball team, your height estimate is far too high.Randomness reduces selection bias because it removes your choices, and your unconscious preferences, from who gets picked.Over many members, the high and low values tend to balance out into a fair picture.Common MistakeRandom does not mean haphazard, such as surveying whoever you happen to bump into.Truly random selection needs a mechanism like random numbers, not just casual convenience.Discrete Vs Continuous DataDiscrete data comes from counting, so it takes separate values with gaps between them.
