ISDS lesson 1 notes

RavshanNovember 11, 2022

ISDS lesson 1 notes

Assalamu alaykum
Today we are going to cover the following topics:

5 number summary

Empirical Rule

Chebyshev's Theorem

The five-number summary

A five-number 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.

Suppose you are given the numbers
200, 250, 200, 300, 300 and 4750
This is how you find the mean, median, lower quartile, upper quartile, range and interquartile range

Watch the following video for more information about the five number summary:

Empirical rule

The empirical rule allows you to find the three intervals within which you'll find 68, 95, and 99.7% of your data. It is called the Empirical Rule because the rule originally came from observations (empirical means “based on observation”).

Try this question yourself. The answer is ........
If you find it difficult, watch the following video:

Chebyshev's Theorem

The inequality has great utility because it can be applied to any probability distribution in which the mean and standard deviations are defined. Its practical usage is similar to the 68–95–99.7 rule, which applies only to normal distributions.
Chebyshev's theorem applies to all data sets, whereas the empirical rule is only appropriate when the data have approximately a symmetric and bell-shaped distribution.