Four things make a problem statistical: the way in which you ask the question, the role and nature of the data, the particular ways in which you examine the data, and the types of interpretations you make from the investigation.
After you analyze your data, you must interpret it in order to provide an answer -- or answers -- to the original question.
This four-step process for solving statistical problems is the foundation of all the activities in this course.
The word statistics may bring to mind polls and surveys, or facts and figures in a newspaper article.
But statistics is more than just a bunch of numbers: Statistics is a problem-solving process that seeks answers to questions through data.
We've selected five classic problems solved in unconventional ways that can help one get a new way to understand the way that data can be misleading and the story on the surface can take people in the wrong direction.(1) THE MONTY HALL PROBLEMSay you're on a game show where there are three doors. Then, you have the option of either staying with your door or switching to the last unopened door. ANSWER: SWITCH This is actually based on a real game show, and the result has been the source of controversy for years.
Essentially, when you first made the selection, you had a one in three chance of correctly selecting the door that had a car behind it.By asking and answering statistical questions, we can learn more about the world around us.Statistics is used every day to help us gain insight into questions that affect our lives: Is our population growing or shrinking? Will eating more fruits and vegetables really make us live longer?Even more, consider the ante in a game of poker, which is a similar system designed to accelerate a winner.Abraham is tasked with reviewing damaged planes coming back from sorties over Germany in the Second World War.A contestant who selects either of the two doors with a goat behind it and then switches will always get the car.Here's a final way to look at it, provided the contestant selected Door #1 Door 1 Door 2 Door 3 Result if Stay #1 Result if Switch Car Goat Goat Car Once the population of an office hits 366 people, it's a certainty that two people in your office have the same birthday, since there are only 365 possible days of birth. Instead of calculating the probability that two people share a birthday, instead calculate the converse, probability that two people don't share a birthday. The probability of the second person not sharing a birthday with the first is 364/365.You obtain data by measuring something, so your measurement methods must be chosen with care.Sampling is one way to collect data; experimentation is another.Switching raised that probability to two in three that you'll select a car.Said another way: A player whose strategy is to always switch will only lose when the door they initially selected has a car behind it.