What is the five-number summary of the distribution?

What is the five-number summary of the distribution?

The five-number summary of a distribution consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest.

What is the five-number summary of a data set?

A five-number summary is especially useful in descriptive analyses or during the preliminary investigation of a large data set. A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.

How many standard deviations to use to identify outliers?

Three standard deviations from the mean is a common cut-off in practice for identifying outliers in a Gaussian or Gaussian-like distribution. For smaller samples of data, perhaps a value of 2 standard deviations (95%) can be used, and for larger samples, perhaps a value of 4 standard deviations (99.9%) can be used.

How does one outlier affect the statistical power?

From the table, it’s easy to see how a single outlier can distort reality. A single value changes the mean height by 0.6m (2 feet) and the standard deviation by a whopping 2.16m (7 feet)! Hypothesis tests that use the mean with the outlier are off the mark. And, the much larger standard deviation will severely reduce statistical power!

Are there any outliers in the Gaussian distribution?

A value that falls outside of 3 standard deviations is part of the distribution, but it is an unlikely or rare event at approximately 1 in 370 samples. Three standard deviations from the mean is a common cut-off in practice for identifying outliers in a Gaussian or Gaussian-like distribution.

How are outliers identified in a scatter plot?

These points are often referred to as outliers. Two graphical techniques for identifying outliers, scatter plotsand box plots, along with an analytic procedure for detecting outliers when the distribution is normal (Grubbs’ Test), are also discussed in detail in the EDA chapter. Box plot construction