If a distribution follows the rule of 68-95-99.7, what can a researcher conclude?
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Meet Mason. He's an average American 40-year-old: 5 foot 10 inches tall and earning $47,000 per year before tax. Show How often would you expect to meet someone who earns 10x as much as Mason? And now, how often would you expect to meet someone who is 10x as tall as Mason? Your answers to the two questions above are different, because the distribution of data is different. In some cases, 10x above average is common. While in others, it's not common at all. So what are normal distributions?Today, we're interested in normal distributions. They are represented by a bell curve: they have a peak in the middle that tapers towards each edge. A lot of things follow this distribution, like your height, weight, and IQ. This distribution is exciting because it's symmetric – which makes it easy to work with. You can reduce lots of complicated mathematics down to a few rules of thumb, because you don't need to worry about weird edge cases. For example, the peak always divides the distribution in half. There's equal mass before and after the peak. Another important property is that we don't need a lot of information to describe a normal distribution. Indeed, we only need two things:
Together, the mean and the standard deviation make up everything you need to know about a distribution. The 68-95-99 ruleThe 68-95-99 rule is based on the mean and standard deviation. It says: 68% of the population is within 1 standard deviation of the mean. How to calculate normal distributionsTo continue our example, the average American male height is 5 feet 10 inches, with a standard deviation of 4 inches. This means: Now for the fun part: Let's apply what we've just learned. What's the chance of seeing someone with a height between between 5 feet 10 inches and 6 feet 2 inches? (That is, between 70 and 74 inches.) It's 34%! We leverage both the properties: the distribution is symmetric, which means chances for (66-70) inches and (70-74) inches are both 68/2 = 34%. Let's try a tougher one. What's the chance of seeing someone with a height between 62 and 66 inches? It's (95-68)/2 = 13.5%. Both outer edges have the same %. And now your final (and hardest test): What's the chance of seeing someone with a height greater than 82 inches? Here, we use also the final property: everything must sum to 100%. So the outer edges (that is, heights below 58 and heights above 82) together make (100% - 99.7%) = 0.3%. Remember, you can apply this on any normal distribution. Try doing the same for female heights: the mean is 65 inches, and standard deviation is 3.5 inches. So, the chance of seeing someone with a height between 65 and 68.5 inches would be: ___. ... ... 34%! It's exactly the same as our first example. It's +1 standard deviation. ConclusionKnowing this rule makes it very easy to calibrate your senses. Since all we need to describe any normal distribution is the mean and standard deviation, this rule holds for every normal distribution in the world! The challenging part, indeed, is figuring out whether the distribution is normal or not. Want to learn more about calibrating your senses and thinking critically? Check out Bayes Theorem: A Framework for Critical Thinking. ADVERTISEMENT ADVERTISEMENT ADVERTISEMENT ADVERTISEMENT Write (Code). Create. Recurse. ... https://neilkakkar.com If you read this far, tweet to the author to show them you care. Tweet a thanks Learn to code for free. freeCodeCamp's open source curriculum has helped more than 40,000 people get jobs as developers. Get started What is the 68In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
What is the range of data values that would allow 68% of the data to fall within the mean?In general, about 68% of the area under a normal distribution curve lies within one standard deviation of the mean. That is, if ˉx is the mean and σ is the standard deviation of the distribution, then 68% of the values fall in the range between (ˉx−σ) and (ˉx+σ) .
What is another name for the 68The empirical rule, also known as the 68-95-99.7 rule, represents the percentages of values within an interval for a normal distribution.
Who discovered the 68It gives how much of the data lies within one, two, or three standard deviations of the mean. The 68–95–99.7 was first discovered and named by Abraham de Moivre in 1733 during his experimentation of flipping 100 fair coins.
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