Unusual results are events that have very low chances of occurrence. They can be identified either with the range rule of thumb or the probability values.
Consider the probability distribution of seat occupancy in a carpool with a mean of 3.5 and a standard deviation of 1.2.
According to the range rule of thumb, the majority of the random variable values must lie within two standard deviations of the mean.
All the remaining data values that fall outside this range are unusual values.
To identify unusual results from probability values, consider the probability distribution of the number of heads in a coin tossed five times.
Since the probability of zero or fewer heads is less than 0.05, those results can be labeled unusual.
Similarly, if the probability of five or more heads is less than 0.05, those results are also unusual.
The cut-off value of two sigmas for random variables and 0.05 for probability is not rigid. It can be decided based on the context of the problem.

unusual results

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances &#8211; an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2&#963;&#160; from the mean, &#956;&#160; is considered unusual.
Maximum unusual value = &#956; + 2&#963;
Minimum unusual value =&#160; &#956; - 2&#963;

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Unusual Results

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In ...

Education

JoVE Core

Statistics

Unit 1

Probability Distributions

KEY TERMS AND CONCEPTS

probability in statistics

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random variables

Random Variables

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probability distributions

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probability histograms

Probability Histograms

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expected value

Expected Value

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binomial probability distribution

Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The ...

poisson probability distribution

Poisson Probability Distribution

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uniform distribution

Uniform Distribution

The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular.
Two ...

normal distribution

Normal Distribution

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z scores and area under the curve

z Scores and Area Under the Curve

z scores are the standardized values obtained after converting a normal distribution into a standard normal distribution. A z score is measured in units ...

applications of normal distribution

Applications of Normal Distribution

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sampling distribution

Sampling Distribution

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central limit theorem

Central Limit Theorem

The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample ...

key terms and concepts

2.9K Views. Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes. According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual. Maximum unusual value = &...

Video: Unusual Results

statistics

JoVE Core Statistics introduces the concepts and application of the collection, analysis, presentation, and interpretation of data to students. These animated lessons provide an understanding of statistics beneficial to students from a wide range of disciplines. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide

6.5 : Unusual Results

6.5 : Unusual Results

6.1 : Probability in Statistics

6.2 : Random Variables

6.3 : Probability Distributions

6.4 : Probability Histograms

6.6 : Expected Value

6.7 : Binomial Probability Distribution

6.8 : Poisson Probability Distribution

6.9 : Uniform Distribution

6.10 : Normal Distribution

6.11 : <em>z</em> Scores and Area Under the Curve

6.12 : Applications of Normal Distribution

6.13 : Sampling Distribution

6.14 : Central Limit Theorem