Learn how to use the Empirical Rule and Chebyshev’s Theorem to describe the distribution of data sets based on their standard deviation. See examples, formulas, and applications of these methods …Mar 12, 2005 · Chebyshev's inequality gives a bound of what percentage of the data falls outside of k standard deviations from the mean. This calculation holds no assumptions about the distribution of the data. If the data are known to be unimodal without a known distribution, then the method can be improved by using the unimodal Chebyshev inequality.(1 - (1 / k2 )). For k = 1, this theorem states that the fraction of all observations having a z score between -1 and 1 is (1 - (1 / 1))2 = 0; of course, this ...A series of free Statistics Lectures in videos. Chebyshev’s Theorem - In this video, I state Chebyshev’s Theorem and use it in a ‘real life’ problem. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step ...How to use Chebyshev's inequality formula? Here are a few examples of the inequality for different values of k: Taking k = 2 as an example, we have 1 - 1/k2 = 1 ...Chebyshev’s inequality theorem provides a lower bound for a proportion of data inside an interval that is symmetric about the mean whereas the Empirical theorem provides the approximate amount of data within a given interval. This is my attempt to put the difference between the two theorems. Let me know if you have difficulties in ...You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Posterior probabilities are computed using: a. the empirical rule. b. Bayes' theorem. a. the empirical rule. b. Bayes' theorem. c. Chebyshev's theorem. d. the classical method.Statistics and Probability. Statistics and Probability questions and answers. Suppose that quiz scores in a beginning statistics class have a mean of 7.4 with a standard deviation of 0.2. Using Chebyshev's Theorem, state the range in which at least 88.9% of the data will reside. Please do not round your answers.Instructions. Enter all the known values. Select the proper units for your inputs and the units you want to get the calculated unknowns in and press Solve. Calculate and solve for any variable () in the Chebyshev's Theorem equation.This article deals with investigations by Pafnuty Chebyshev and Samuel Roberts in the late 1800s, which led them independently to the conclusion that for each curve that can be drawn by four bar linkages, there are always three linkages describing the same curve. These different linkages resulting in the same curve can be called cognate linkages.15 minutes. 1 pt. True or False: The percentages obtained by Chebyshev's Theorem are conservative lower estimates. The percent of data between any two boundaries is usually much more than the number given by the Theorem. True. Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:. Here, K is any positive integer greater than one. For example, if K is 1.5, at least 56% of the data values lie within 1.5 standard deviations from the mean for a dataset. If K is 2, at least 75% of the …It should be emphasized that, although Chebyshev’s Inequality proves the Law of Large Numbers, it is actually a very crude inequality for the probabilities involved. However, its strength lies in the fact that it is true for any random variable at all, and it allows us to prove a very powerful theorem.Jan 1, 2014 · Chebyshev was the first to prove that π(n) grows on the order \(\frac{n} {\log n}\). Chebyshev’s methods were ingenious but entirely elementary. Given the truly elementary nature of his approach, it is quite impressive how close his result is to the prime number theorem. Here is Chebyshev’s result.Mar 12, 2005 · Chebyshev's inequality gives a bound of what percentage of the data falls outside of k standard deviations from the mean. This calculation holds no assumptions about the distribution of the data. If the data are known to be unimodal without a known distribution, then the method can be improved by using the unimodal Chebyshev inequality.Nov 15, 2012 · This problem is a basic example that demonstrates how and when to apply Chebyshev's Theorem. This video is a sample of the content that can be found at http... As a result, Chebyshev's can only be used when an ordering of variables is given or determined. This means it is often applied by assuming a particular ordering without loss of generality \ ( (\)e.g. \ (a \geq b \geq c),\) and examining an inequality chain this applies. Two common examples to keep in mind include the following:Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Chebyshev's Theorem - In t...Sep 11, 2014 ... The situation for explicit integration in \eta is complementary to that in t. ... We also show that our method may be used to study more realistic ...Jun 30, 2021 · So Chebyshev’s Theorem implies that at most one person in four hundred has an IQ of 300 or more. We have gotten a much tighter bound using additional information—the variance of \(R\)—than we could get knowing only the expectation. 1 There are Chebyshev Theorems in several other disciplines, but Theorem 19.2.3 is the only one we’ll ... Jun 19, 2019 ... Chebyshev's theorem is a very useful tool for finding a lower bound for the percent of data within a given interval. In this video, we use ...It should be emphasized that, although Chebyshev’s Inequality proves the Law of Large Numbers, it is actually a very crude inequality for the probabilities involved. However, its strength lies in the fact that it is true for any random variable at all, and it allows us to prove a very powerful theorem.Chebyshev's Theorem: 3 standard deviations. 89%. Chebyshev's Theorem: 4 standard devaluation. 94%. Chebyshev's Theorem Equation. 1- (1-k^2) standard score (z score) the number of standard deviations a number is from the mean. Study with Quizlet and memorize flashcards containing terms like Empirical Rule: 1 standard deviation, Empirical Rule: 2 ... Apr 1, 2016 ... This is just a few minutes of a complete course. Get full lessons & more subjects at: http://www.MathTutorDVD.com.Apr 14, 2018 · As you can see Chebyshev’s inequality gives an only upper limit of probability deviation. Probability can’t be more than this value no matter what. The law of large numbers is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a …Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation: Here, K is any positive integer greater than one. For example, if K is 1.5, at least 56% of the data values lie within 1.5 standard deviations from the mean for a dataset. May 28, 2023 · The Empirical Rule is an approximation that applies only to data sets with a bell-shaped relative frequency histogram. It estimates the proportion of the measurements that lie within one, two, and three standard deviations of the mean. Chebyshev’s Theorem is a fact that applies to all possible data sets. The Bertrand-Chebyshev Theorem was first postulated by Bertrand in 1845 1845. He verified it for n < 3000000 n < 3 000 000 . It became known as Bertrand's Postulate . The first proof was given by Chebyshev in 1850 1850 as a by-product of his work attempting to prove the Prime Number Theorem .The principal result of this section is the Chebyshev alternation theorem (also called the Chebyshev equioscillation theorem), which gives necessary and sufficient conditions for a polynomial \(p\in \mathscr {P}_n\) to be a polynomial of best approximation to a given continuous function f(x) on [a, b] (on a more general compact set Q).This …Chebyshev’s inequality, in probability theory, a theorem that characterizes the dispersion of data away from its mean (average). The general theorem is attributed to the 19th-century Russian mathematician Pafnuty Chebyshev, though credit for it should be shared with the French mathematician.According to Chebyshev's theorem, how many standard deviations from the mean would make up the central 60% of scores for this class? [What are the corresponding grades? Answer the same questions for central 80%. Do these values capture more than the desired amount? Does this agree with Chebyshev's theorem?]There are at least two theorems known as Chebyshev's theorem. The first is Bertrand's postulate, proposed by Bertrand in 1845 and proved by Chebyshev using …Chebyshev's Theorem: Let X X be a discrete random variable with finite mean μx μ x and standard deviation σx σ x. Let k k be greater than 1 1. Then the probability that X X is more than k k standard deviations from the mean, μX μ …Dec 9, 2014 · This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original articleUsing Chebyshev's theorem, calculate the minimum proportions of computers that fall within 2 standard deviations of the mean. Step 1: Calculate the mean and standard deviation. The mean of the ... Feb 12, 2024 · The Chebyshev Inequality. Instructor: John Tsitsiklis. Transcript. Download video. Download transcript. MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a …By Chebyshev’s Theorem, at least 3/4 of the data are within this interval. Since 3/4 of 50 is 37.5, this means that at least 37.5 observations are in the interval. But one cannot take a fractional observation, so we conclude that at least 38 observations must lie inside the interval (22,34).Feb 27, 2008 ... The bottomline is, Chebyshev's rule applies regardless of the distribution. If I am not wrong, it is an estimation and 0 % of the ...Cognate Linkages the Roberts – Chebyshev Theorem 509 Fig. 5. Chebyshev linkages Fig. 6. Extended Chebyshev linkage Chebyshev had already shown that in order to get the best approximation of a straight line the linkage must satisfy two conditions. First the distance CC 1 must be equal to 1/3 (AC + A 1C 1 + AA 1). The second says that the ...Feb 7, 2024 · Using Chebyshev’s Theorem, at least what percentage of adults have a score between 55 and 145? Problem 6: The mean weight of a package handled by Speedy Delivery Inc. is 18 lbs with a standard deviation of 7 lbs. Using Chebyshev’s Theorem, at least what percentage of packages will lie within 2 standard deviations of the mean? Statistics and Probability questions and answers. Select all that apply Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply. Chebyshev's theorem applies to any set of values. Chebyshev's theorem works for symmetrical, bell-shaped distributions. 15 minutes. 1 pt. True or False: The percentages obtained by Chebyshev's Theorem are conservative lower estimates. The percent of data between any two boundaries is usually much more than the number given by the Theorem. True. 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. The Sharpe ratio measures the extra reward per unit of risk Instructions: This Chebyshev's Rule calculator will show you how to use Chebyshev's Inequality to estimate probabilities of an arbitrary distribution. You can estimate the probability that a random variable X X is within k k standard deviations of the mean, by typing the value of k k in the form below; OR specify the population mean \mu μ ... Statistics Chebyshev's Theorem in Urdu Hindi What is Chebyshev's TheoremFeb 23, 2017 · 1. Chebyshev's inequality says that. P(|X − μ| > kσ) ≤ 1 k2 P ( | X − μ | > k σ) ≤ 1 k 2. where μ μ is the mean of X X and σ σ is its standard deviation. This is the probability of the random variable being more than k k standard deviations from the mean, and note that its maximum value goes down as k k gets large, as you would ...Chebyshev’s theorem is a valuable tool in probability theory and is widely used in statistical analysis to make general statements about the spread of data. Chebyshev’s Theorem applies to all probability distributions where you can calculate the mean and standard deviation, while the Empirical Rule applies only to the normal …切比雪夫定理（Chebyshev's theorem）：适用于任何数据集，而不论数据的分布情况如何。 与平均数的距离在z个标准差之内的数值所占的比例至少为(1-1/z 2)，其中z是大于1的任意实数。. 至少75%的数据值与平均数的距离在z=2个标准差之内；Lets use Chebyshev's inequality to make a statement about the bounds for the probability of being with in 1, 2, or 3 standard deviations of the mean for all random variables. If we de ne a = k where = pVar(X) then. Var(X) 1 P(jX E(X)j k ) = k2 2 k2. Sta 111 (Colin Rundel) Lecture 7. Lecture 7. Jun 19, 2019 ... Chebyshev's theorem is a very useful tool for finding a lower bound for the percent of data within a given interval. In this video, we use ...Teorema Chebyshev (4) • Contoh Penggunaan Teorema Chebyshev: Peubah acak X mempunyai rataan µ=8 dan variansi σ2 = 9, serta distribusi peluang tidak diketahui. Tentukan P(-4< x < 20 ). Global Development Learning Network 5 • Jawab:Use Chebyshev's theorem to find what percent of the values will fall between 123 and 179 for a data set with mean of 151 and standard deviation of 14. We subtract 151-123 and get 28, which tells us that 123 is 28 units below the mean. We subtract 179-151 and also get 28, which tells us that 151 is 28 units above the mean. Chebyshev's Theorem Formula. Look at the formula which are given below about Chebyshev's Theorem. Here, P = probability of an event. X = random variable. E(X) = expected value of our event. σ² = variance of our event. k = boundary of the result. Chebyshev's Inequality Proof . As per Chebyshev's Theorem the probability that an …Jun 11, 2020 · As far as I can tell, nothing has gone wrong. Chebyshev's inequality doesn't tell you anything if what you're looking at is within one standard deviation of the mean ... probability-limit-theorems. Featured on Meta Site maintenance - Saturday, February 24th, 2024, 14:00 - 22:00 UTC (9 AM ...Chebyshev's Theorem. The Russian mathematician P. L. Chebyshev (1821- 1894) discovered that the fraction of observations falling between two distinct values, whose differences from the mean have the same absolute value, is related to the variance of the population. Chebyshev's Theorem gives a conservative estimate to the above percentage.You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Posterior probabilities are computed using: a. the empirical rule. b. Bayes' theorem. a. the empirical rule. b. Bayes' theorem. c. Chebyshev's theorem. d. the classical method.In this video, we demonstrate how to use Chebyshev's theorem to find an interval that captures at least 94% of the data. This video is part of the content av...Using the accompanying table of data, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000 cells/μ L.) Using Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within 3 standard deviations of the mean?Example 1: Use Chebyshev’s Theorem to find what percentage of values will fall between 30 and 70 for a dataset with a mean of 50 and standard deviation of 10. First, determine the value for k. We can …This article deals with investigations by Pafnuty Chebyshev and Samuel Roberts in the late 1800s, which led them independently to the conclusion that for each curve that can be drawn by four bar linkages, there are always three linkages describing the same curve. These different linkages resulting in the same curve can be called cognate linkages.Jun 26, 2019 · The proof of Chebyshev’s inequality relies on Markov’s inequality. Note that |X– μ| ≥ a is equivalent to (X − μ)2 ≥ a2. Let us put. Y = (X − μ)2. Then Y is a non-negative random variable. Applying Markov’s inequality with Y and constant a2 gives. P(Y ≥ a2) ≤ E[Y] a2. Now, the definition of the variance of X yields that.Pafnuty Lvovich Chebyshev (Russian: Пафну́тий Льво́вич Чебышёв, IPA: [pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof]) (16 May [O.S. 4 May] 1821 – 8 December [O.S. 26 November] 1894) was a Russian mathematician and considered to be the founding father of Russian mathematics.. Chebyshev is known for his fundamental contributions to the fields of probability, …Jun 30, 2016 · Jason Gibson describes how and when to use Chebyshev's Theorem in statistical calculations. He also demonstrates three practice problems using Chebyshev's Theorem. Chapter 1: Chebyshev's Theorem Jun 3, 2023 ... Chebyshev's theorem is a statistical theorem that applies to any distribution, whether symmetric or asymmetric. It provides an estimate of ...Chebyshev's theorem. 08-S1-Q5. Analysis, polynomials, turning point, C1. q. [STEP I 2008 Question 5 (Pure)]. Read more. Useful Links. Underground Mathematics ...This video shows how to solve applications involving Chebyshev's Theorem.This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Suppose that quiz scores in a beginning statistics class have a mean of 7.2 with a standard deviation of 0.2. Using Chebyshev's Theorem, state the range in which at least 88.9 % of the data will reside.Free Chebyshevs Theorem Calculator - Using Chebyshevs Theorem, this calculates the following: Probability that random variable X is within k standard deviations of the mean. How many k standard deviations within the mean given …15 minutes. 1 pt. True or False: The percentages obtained by Chebyshev's Theorem are conservative lower estimates. The percent of data between any two boundaries is usually much more than the number given by the Theorem. True.Oct 13, 2020 ... The Chebyshev's theorem presupposes that in the process of a probability distribution, almost every element is going to be very close to the ...Cite this chapter. Chandrasekharan, K. (1968). Chebyshev’s theorem on the distribution of prime numbers. In: Introduction to Analytic Number Theory. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, vol 148.in (n;2n], whereas Chebyshev’s theorem counts primes in (0;n]. This problem is surmountable: Exercise 8. The goal of this exercise is to deduce the upper bound in Chebyshev’s theorem. (a)Prove that there exists a constant csuch that ˇ(2x) ˇ(x) c x logx for all real numbers x 2. Empirical Rule/Chebyshev's Theorem Worksheet 1) Adult IQ scores have a bell - shaped distribution with a mean of 100 and a standard deviation of 15. Use the Empirical Rule to find the percentage of adults with scores between 70 and 130. 2) Lengths of pregnancies of humans are normally distributed with a mean of 265 days and a standard deviation of 10 …Example 2 Chebyshev Inequality Theorem Calculator The daily production of electric motors at a certain factory averaged 120, with a standard deviation of 10. a.Jun 11, 2020 · As far as I can tell, nothing has gone wrong. Chebyshev's inequality doesn't tell you anything if what you're looking at is within one standard deviation of the mean ... probability-limit-theorems. Featured on Meta Site maintenance - Saturday, February 24th, 2024, 14:00 - 22:00 UTC (9 AM ...Feb 12, 2024 · The Chebyshev Inequality. Instructor: John Tsitsiklis. Transcript. Download video. Download transcript. MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a …Free Chebyshevs Theorem Calculator - Using Chebyshevs Theorem, this calculates the following: Probability that random variable X is within k standard deviations of the mean. How many k standard deviations within the mean given …This lecture will explain Chebyshev's inequality with several solved examples. A simple way to solve the problem is explained.Other videos @DrHarishGarg Cheb...This theorem was proved by P.L. Chebyshev in 1854 (cf. [1]) in a more general form, namely for the best uniform approximation of functions by rational functions …According to Chebyshev's theorem, how many standard deviations from the mean would make up the central 60% of scores for this class? [What are the corresponding grades? Answer the same questions for central 80%. Do these values capture more than the desired amount? Does this agree with Chebyshev's theorem?]Jun 30, 2021 · So Chebyshev’s Theorem implies that at most one person in four hundred has an IQ of 300 or more. We have gotten a much tighter bound using additional information—the variance of \(R\)—than we could get knowing only the expectation. 1 There are Chebyshev Theorems in several other disciplines, but Theorem 19.2.3 is the only one we’ll ... Sep 26, 2006 ... 3 Proof of Chebyshev's Theorem. We now prove Chebyshev's Theorem. The first part of the proof is due to the Chebyshev. Polynomial, where we ...Teorema Chebyshev (4) • Contoh Penggunaan Teorema Chebyshev: Peubah acak X mempunyai rataan µ=8 dan variansi σ2 = 9, serta distribusi peluang tidak diketahui. Tentukan P(-4< x < 20 ). Global Development Learning Network 5 • Jawab:Pafnuty Chebyshev's parents were Agrafena Ivanova Pozniakova and Lev Pavlovich Chebyshev. Pafnuty was born in Okatovo, a small town in western Russia, south-west of Moscow. ... Twenty years later Chebyshev published On two theorems concerning probability which gives the basis for applying the theory of probability to statistical data, ...Oct 18, 2019 · Chebyshev’s inequality is an extremely useful theorem when combining with other theorem and it is a bedrock of confidence interval. In this blog, I will illustrate the theorem and how it works ... Chebyshev's inequality theorem is one of many (e.g., Markov’s inequality theorem) helping to describe the characteristics of probability distributions. The theorems are useful in detecting outliers and in clustering data into …According to Chebyshev's inequality, at least (1-1/k^2) of the distribution's …. Apply Chebyshev's Theorem to find the least possible fraction of the numbers in a data set lying within standard deviations of the mean. At least of all numbers must lie within (Type an integer or a simplified fraction.) standard deviations from the mean.
exists, then it is 1 (Havil 2003, p. 186). Derbyshire's (2004, p. 124) statement that in 1850, Chebyshev also showed that cannot differ from by more than approximately 10% is therefore correct only for sufficiently large .. Hadamard and de la Vallée Poussin independently proved the prime number theorem in 1896 by showing that the Riemann …. Wifi locations near me
How to use Chebyshev's inequality formula? Here are a few examples of the inequality for different values of k: Taking k = 2 as an example, we have 1 - 1/k2 = 1 ...Chebyshev’s Theorem is named after the Russian mathematician Pafnuty Chebyshev and is a fundamental concept in probability and statistics. It provides a way to estimate the minimum percentage of data points that fall within a certain range of standard deviations from the mean in any data set.Equioscillation theorem. In mathematics, the equioscillation theorem concerns the approximation of continuous functions using polynomials when the merit function is the maximum difference ( uniform norm ). Its discovery is attributed to Chebyshev. [1] Chebyshev’s Theorem Formula: If the mean μ and the standard deviation σ of the data set are known then the 75% to 80 % points lie in between two standard deviations. The probability that x is within the K standard deviation is determined by the following formula: Pr ( ∣X − μ∣ < kσ ) ≥ 1 − 1 / k^2. Where: P denoted the ...Jason Gibson describes how and when to use Chebyshev's Theorem in statistical calculations. He also demonstrates three practice problems using Chebyshev's Theorem. Chapter 1: Chebyshev's Theorem icon angle down. Start time: 00:00:00; End time: 00:06:30; Chapter 2: Chebyshev's Theorem Practice ProblemsChebyshev’s Theorem. If $\mu$ and $\sigma$ are the mean and the standard deviation of a random variable X, then for any positive constant k the probability is at least $1- \frac{1}{k^2}$ that X will take on a value within k standard deviations of …Jun 8, 2021 · Step-4: Apply the Chebyshev’s Theorem to find the required probability: ≥ 1-1/k 2 ≥ 1-(1/4) ≥ 3/4 ≥ 0.75. Step-5: Present the results. Therefore, the lower bound of the probability that the productivity lies between 40 and 60 is equal to 0.75. Numerical Example-2: A symmetric die is thrown 600 times.Jun 17, 2021 ... In this video, we'll be discussing the empirical rule and Chebyshev's theorem. We'll also be discussing how they can be used to calculate ...There are at least two theorems known as Chebyshev's theorem. The first is Bertrand's postulate, proposed by Bertrand in 1845 and proved by Chebyshev using ...In this video we discuss what is, and how to use Chebyshev's theorem and the empirical rule for distributions in statistics. We define both of these topics ...Jun 8, 2021 · Step-4: Apply the Chebyshev’s Theorem to find the required probability: ≥ 1-1/k 2 ≥ 1-(1/4) ≥ 3/4 ≥ 0.75. Step-5: Present the results. Therefore, the lower bound of the probability that the productivity lies between 40 and 60 is equal to 0.75. Numerical Example-2: A symmetric die is thrown 600 times.Chebyshev's Theorem for two standard deviations ( = 2) is calculated like this: )) = .7500. This is interpreted to mean that at least .75 of the observations will fall between -2 and +2 standard deviations. In fact, for the example distribution .891 of the observations fall with that range. It is the case the 7.5 is less than or eaual to .891. Jun 19, 2019 ... Chebyshev's theorem is a very useful tool for finding a lower bound for the percent of data within a given interval. In this video, we use ...Please note the mistake in subtraction at about 4 minutes. 26 - 10.5 is 15.5 -- I accidentally wrote 25.5 when doing that. Thanks for point out the error!!...Example 1: Use Chebyshev’s Theorem to find what percentage of values will fall between 30 and 70 for a dataset with a mean of 50 and standard deviation of 10. First, determine the value for k. We can …May 10, 2019 · Chebyshev's theorem is a very useful tool for finding a lower bound for the percent of data within a given interval. In this video, we use the results of the...Jun 26, 2019 · The proof of Chebyshev’s inequality relies on Markov’s inequality. Note that |X– μ| ≥ a is equivalent to (X − μ)2 ≥ a2. Let us put. Y = (X − μ)2. Then Y is a non-negative random variable. Applying Markov’s inequality with Y and constant a2 gives. P(Y ≥ a2) ≤ E[Y] a2. Now, the definition of the variance of X yields that.Chebyshev’s inequality (other wise known as Chebyshev’s theorem)[1] was designed to determine a lower bound of the percentage of data that exists within k number of standardFour Problems Solved Using Chebyshev's Theorem. Chebyshev’s theorem states that the proportion or percentage of any data set that lies within k standard deviation of the mean where k is any positive integer greater than 1 is at least 1 – 1/k^2. Below are four sample problems showing how to use Chebyshev's theorem to solve word problems.6. Answer key. 1. Chebyshev's theorem can be applied to any data from any distribution. So, the proportion of data within 2 standard deviations of the mean is ....