Understanding Chebyshev’s Theorem?

What it – How it works

By Dr. David Edward Marcinko MBA CMP™


The rule is often called Chebyshev’s theorem, about the range of standard deviations around the mean, in statistics www.HealthDictionarySeries.org

The inequality has great utility because it can be applied to any probability distribution in which the mean and variance are defined. But first, let us review the Empirical Rule.

Empirical Rule

In probability theory, the central limit theorem (CLT) states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying


Central Limit Theorem



What is a Galton Board?


Chebyshev’s Theorem

The Russian mathematician P.L. Chebyshev (1821-1894) proved a theorem which is valid for any distribution of data:

For any number k greater than 1, at least 1-1/k2 of the data will fall within k standard deviations of the mean. This theorem produces a few useful rules:

  • no information can be obtained on the fraction of values falling within 1 standard deviation of the mean
  • at least 75% will fall within 2 standard deviations
  • at least 88.8 % will fall within 3 standard deviations

The following figure is a graphical presentation of these rules.


Chebyshev’s Theorem: The proportion of any distribution that lies within k standard deviations of the mean is at least 1 – (1/k2), where k is any positive number larger than 1. This theorem applies to all distributions of data.


OK; so basically Chebyshev’s theorem states that 75% of your data will lie within 2 standard deviations of the mean and that 89% of your data will lie within 3 standard deviations of the mean.

And, I believe that this theorem is much more precise than the Empirical Rule, which assumes normality and can be off.


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The GOLD and Gold Miners Chart-Book

By Merk Investments


READ BOOK: https://www.merkinvestments.com/downloads/2022-09-01-gold-chart-book.pdf




Thank You


CITE: https://www.r2library.com/Resource/Title/082610254


PODCAST: Patient Centricity in Value Based Care?

By Eric Bricker MD


Dr. Sachin MD MBA Jain wrote an outstanding article on Value Based Care in the April 12, 2022 issue of Forbes stating that the Patient Must Come First in Value Based Care.




Thank You


RELATED PODCAST: https://medicalexecutivepost.com/2021/12/13/podcasts-the-case-against-value-based-care/

RELATED: https://www.amazon.com/Financial-Management-Strategies-Healthcare-Organizations/dp/1466558733/ref=sr_1_3?ie=UTF8&qid=1380743521&sr=8-3&keywords=david+marcinko

MORE: https://www.amazon.com/Business-Medical-Practice-Transformational-Doctors/dp/0826105750/ref=sr_1_9?ie=UTF8&qid=1448163039&sr=8-9&keywords=david+marcinko

ADDITIONAL: https://www.amazon.com/Hospitals-Healthcare-Organizations-Management-Operational/dp/1439879907/ref=sr_1_4?s=books&ie=UTF8&qid=1334193619&sr=1-4



By Dr. David Edward Marcinko MBA


World Gratitude Day is a timely opportunity to give your employees their deserved props—beyond an ordinary thumbs-up emoji. And, how you celebrate the day is limited only by your imagination.

Some people write thank you notes to those they appreciate. Some make a point of having “gratitude dinners” with family members. And others start a gratitude journal in which they record what they’re grateful for.


Dignity Health


We’re all human, and at Workhuman, they get that. Workhuman’s employee recognition solution, Social Recognition, helps foster employee appreciation—something that strengthens teams, reduces turnovers, and drives business forward.

Yep, a little “Thank you” goes a long way.




The Seasons, the Equinox, and the Solstices


Today, in 2021, the autumnal equinox will also take place at 3:21 p.m. EDT and marks the moment the sun’s rays are shining directly on the equator. It’s called the equinox because daytime and nighttime are equal lengths. The winter solstice, which occurs on Dec. 21, will be the shortest day of the year and marks the start of winter.




MORE: https://www.daysoftheyear.com/days/world-gratitude-day/


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