Statistics Problem Solving

That means that the probability that two people in the office share a birthday is 1 -- 0.4927 = 0.5073, or 50.7%.A gambler has a certain amount of money ("B") and is playing a game of chance with some win probability less than 1.When B= 00 and N=4, for example, he'll gamble 0 each time going forward. If our gambler sounds like something of an idiot, know that this is actually a rather common betting strategy.

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Data must be organized, summarized, and represented properly in order to provide good answers to statistical questions.

Also, the data you collect usually vary (i.e., they are not all the same), and you will need to account for the sources of this variation.

Every time he wins, he raises his stake to a certain fraction, 1/N, of his bankroll, where N is a positive number. ANSWER: HE'LL LOSE EVERYTHING When it comes down to it, if our gambler bets 1/N of his bankroll each time and then maintains the amount as he loses, the gambler is N losing bets in a row away from bankruptcy.

The gambler doesn't reduce his stake when he loses Every time he wins, he'll raise his stake to $B/N, or his bankroll divided by N. Assuming that the player keeps on playing and there is some chance that the player can lose -- we are gambling, after all -- then the player remains N losing bets away from a broken bank each time.

Even a rudimentary look at probability can give new insights about how to interpret data.

Simple thought experiments an can give new insight into the different ways misunderstanding of statistics can distort the way we perceive the world. The host says that once you pick a door, he'll open one of the doors you didn't pick to reveal a goat.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.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.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.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.He has to review the damage of the planes to see which areas must be protected even more.Abraham finds that the fuselage and fuel system of returned planes are much more likely to be damaged by bullets or flak than the engines. ANSWER: PROTECT THE PARTS THAT DON'T HAVE DAMAGE Abraham Wald, a member of the Statistical Research Group at the time, saw this problem and made an unconventional suggestion that saved countless lives.

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