This coming week there are big primaries with lot of delegates up for grabs in New York. It seems from the polls that the both Trump and Clinton are ahead. How reliable are those polls? There are many ways to answer that question and it really depends on many complex considerations such as how the poll was taken, how many people were sampled etc. But without going into all of that there is something each of us can look up to determine reliability. Each poll comes with a margin of error which tells us that we can expect the poll is correct give or take the few points of margin of error. We ought to take note of those numbers. Whilst the poll number itself is helpful it does not tell us the entire story. When we take the margin of error into account we get a more accurate picture of what the poll is really saying.
The main number of the poll is like the average. We like to use the average a lot because it conveys a summary of a population we are interested in. Politicians love talking about the “average American”. In sports you have Batting Averages and Average Scoring Margins amongst others. These are all very valuable but do not convey the entire picture. As was mentioned in a previous post the medium is also an important number to know. You can read that more about the median and see its accompanying app here. However, even with knowing the mean and the medium we do not have the entire story. We need another piece of information and that is how variable (spread out) the population is around the mean.
Technically the income of the average American family income is $53,657 per year. But the entire population might be very spread out around that number and therefore that summary statistic does not give us enough information about most Americans. See if the population is very spread out you could have a huge chunk earning considerably less or more than $53,657. Whereas if the population is tightly clustered around the mean than the $53,657 tells us a great deal about the population as a whole.
The Standard Deviation is a number which tells us how spread out or how closely clustered a population is around its mean. A higher number of Standard Deviation tells us that the populations is more spread out and a lower number tells us it is more tightly clustered around the mean.
The Standard Deviation and the Margin of Error are similar to each other. They both tell us how reliable the main number — the poll or the mean — is, and how much we can expect the actual result to vary.
Thus, whether we are talking about polls or general statistics we should be careful to look for more than just the headline number and ask for the median and the standard deviation so that we can get a more accurate picture.