Percentages are often misleading, even in the simplest of situations, like flipping a coin, and definitely in more complex situations, like poll figures before an election. But why does this happen?
Figuring out percentages and probabilities is a complex task, and one which can lead to misconceptions. (Image: Gearstd/Shutterstock)
Judging the Fairness of a Coin
Let ’ s start with a position that ’ randomness reasonably easily. Let ’ s flip a coin. The first gear question we want to ask is : Is the coin fair ? Will you get heads 50 % of the time ?
Say you flipped the mint 10 times and came up with 3 heads. therefore, is the mint fair ? Well, the decision is “ possibly ”. And that ’ second because random stuff happens .
How frequently can you expect to get heads if you flip a bonny mint 10 times ? You expect to get 0 heads about 0.1 % of the time, 1 head about 1 % of the fourth dimension, 2 heads about 4 % of the time, 3 heads about 12 % of the meter, 4 heads about 21 % of the time, and last, 5 heads only 25 % of the time. For 6 through 10 heads, it ’ randomness good the opposition .
The probability of getting heads clusters closer around the 50% mark as the number of tosses increases. (Image: Peter Hermes Furian/Shutterstock) It shows that when you flip a fair mint 10 times, you can pretty a lot get any consequence with fair probability. so, if you do flip a mint 10 times and see 3 heads, that ’ s a pretty common result and you can ’ deoxythymidine monophosphate conclude that the coin is unfair.
What if the same experiment is done by flipping the coin 1000 times ? If you flip a coin 1000 times, it ’ s most probably that you ’ ll get heads somewhere between 47 and 53 percentage of the times .
so what ’ s the message here ? The message is that using statistics doesn ’ triiodothyronine well answer a question. If a mint is flipped 10 times, the result can be anything from 0 to 10 heads. flush if the coin is flick 1000 times, you can calm expect to get a count in the 47 to 53 % compass. That is still not a beneficial enough measurement to determine if the mint wasn ’ triiodothyronine unfair by 51 to 49 percentage .
This is a transcript from the television series Understanding the Misconceptions of Science. Watch it now, Wondrium .
Election Predictions and Polling Statistics
The bottom line is that if you want to determine a probability, you need to gather a bunch of statistics. One invest where statistics is used a bunch is in elections. Prior to an election, not every person in the nation can be asked who they ’ ll vote for. So pollsters call a few people to see how they ’ re going to vote .
On the other hand, there are hundreds of millions of possible voters. If only a couple of thousand people are asked, that ’ s not good enough to get an accurate calculate of how the vote will turn out. That ’ sulfur why thoroughly newspapers give a margin of error. That ’ s an undertake to estimate the crop of possible outcomes .
Learn more about evocation within poll and scientific reasoning .
Sample Selection for a Fair Poll
however, the process is much trickier. Suppose, like is often in the lawsuit of US presidential election, the actual vote will be very close—very about 50-50. It ’ s pretty easy to imagine asking 1000 voters and getting an consequence, for exercise, that the people you polled came out for the Republicans by an 80-20 rent.
immediately, that might sound impossible, but suppose that the people that were asked were attending a National Rifle Association convention. You can never be sure, but it seems reasonable that NRA members might preferentially vote Republican. If you did the same exert at a Greenpeace convention, you might find the opposite, with a majority of people being polled vote democratic .
Exit polls must pick an unbiased sample for the survey, if they want to reflect the voting pattern accurately. (Image: Sergieiev/Shutterstock)
The point here is that it is extremely significant when you do a statistical survey to pick an unbiased sample. In the case of polling for elections, you must select a small group of people who are similar, on average, to the typical voters .
historically, older, white, rural voters are more probably to go to the polls than younger, urban, ethnically divers voters. And pollsters have to take all of that into account in order to get an accurate prediction .
The thing to keep in mind is that when you read a poll, try to find out if there are problems with how the poll was conducted. If the count of people asked was pretty little, you have reasons to be fishy of the decision. similarly, if the poll was conducted by an arrangement that might select a group of people who differ from the probably voters, suspicions must arise there, besides .
thus, probabilities and poll results are things that are statistically complex and require a draw of psychoanalysis and a set of data to be properly .
Learn more about the concept of randomness and its quantification through probability .
Common Questions about Percentages and Predictions
Q. What are the chances of getting two heads if you flip a fair coin twice? If you flip a fair coin doubly, the potential outcomes are heads-heads, heads-tails, tails- heads, and tails-tails. thus, the prospect of getting two heads is one in four, or 25 %.
Q. What are the chances of getting 5 heads or 5 tails in 10 flips of a coin? If you flip a fair mint 10 times, you can get 0 heads about 0.1 % of the clock, 1 capitulum about 1 % of the time, 2 heads about 4 % of the prison term, 3 heads about 12 % of the time, 4 heads about 21 % of the time, and 5 heads about 25 % of the time. therefore, the chances of getting 5 heads is about 1 in 4. Q. Can you know that a coin is fair if you look at the result of flipping it 1000 times? If you flip a mint 1000 times, it ’ s most probably that you ’ ll get heads somewhere between 47 and 53 % of the times. That is silent not a dear enough measurement to determine if the coin wasn ’ metric ton unfair by 51 to 49 percentage. Q. When looking at poll, what should the reader keep in mind? Polls predicting election results need to be conducted cautiously. If the total of people asked was pretty little, you have reasons to be leery of the ending. similarly, if the poll was conducted by an constitution that might select a group of people who differ from the probable voters, you should be leery there, excessively .
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