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VrcAcademy - Statistics, R languages and Operations

Details: VrcAcademy is a group of experienced tutors/teachers who provide you concise, easy to grasp information in form of tutorials. We also provide you the calculators and formulas to make your education journey easy and fast.

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Weibull Distribution Examples - Step by Step Guide

Details: Weibull Distribution. In this tutorial we will discuss about the Weibull distribution and examples. Weibull distribution is a continuous probability distribution.Weibull distribution is one of the most widely used probability distribution in reliability engineering.. This tutorial help you to understand how to calculate probabilities related to Weibull distribution and step by step guide on

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Discrete Uniform Distribution examples in Statistics

Details: Discrete uniform distribution. In this tutorial we will discuss some examples on discrete uniform distribution and learn how to compute mean of uniform distribution, variance of uniform distribution and probabilities related to uniform distribution.

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Continuous Uniform Distribution Examples in Statistics

Details: Continuous Uniform Distribution. The continuous uniform distribution is the simplest probability distribution where all the values belonging to its support have the same probability density. It is also known as rectangular distribution. This tutorial will help you understand how to solve the numerical examples based on continuous uniform

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Chi-square Test for variance examples - VrcAcademy

Details: In this tutorial we will discuss a method for testing a claim made about the population variance σ 2 or population standard deviation σ. To test the claim about the population variance or population standard deviation we use chi-square test. In this tutorial we will discuss some numerical examples using six steps approach used in hypothesis

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Exponential Distribution Examples in Statistics - VrcAcademy

Details: Solution. Let X denote the time (in hours) required to repair a machine. Given that X is exponentially distributed with λ = 1 / 2. The pdf of X is f(x) = λe − λx, x > 0 = 1 2e − x / 2, x > 0. The distribution function of X is F(x) = P(X ≤ x) = 1 − e − x / 2. a. The probability that a repair time exceeds 4 hours is.

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Summary statistics for ungrouped data - VrcAcademy

Details: Summary statistic for ungrouped data. Summary statistic summarize and provide information about the sample data. It includes the minimum value of the data, first quartile ( Q 1 ), median (i.e., Q 2 ), mean ( x ¯ ), third quartile ( Q 3) and the minimum value of the data. maximum value ( max ).

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Variance and standard deviation for ungrouped data

Details: Formula. Sample variance of X is denoted by s x 2 and is given by. s x 2 = 1 n − 1 ∑ i = 1 n ( x i − x ¯) 2 = 1 n − 1 ( ∑ i = 1 n x i 2 − ( ∑ i = 1 n x i) 2 n) where, x ¯ = 1 n ∑ i = 1 n x i is the sample mean. The sample standard deviation of X is defined as the positive square root of the sample variance. The sample standard

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Bowleys Coefficient of skewness for grouped data - VrcAcademy

Details: Bowley’s Coefficient of Skewness for grouped data. Skewness is a measure of symmetry. The meaning of skewness is “lack of symmetry”. Skewness gives us an idea about the concentration of higher or lower data values around the central value of the data. For a symmetric distribution, the two quartiles namely Q 1 and Q 3 are equidistance from

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Mean median and mode for ungrouped data - VrcAcademy

Details: mean median mode, mean median mode definition,mean median mode formula, mean median mode calculator, mean median mode examples, mean median mode relation

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Mean median mode for grouped data calculator (Frequency

Details: Let x 1, x 2, ⋯, x n have frequencies f 1, f 2, ⋯, f n respectively, then the Harmonic Mean is given by. M e a n = X ¯ = 1 N ∑ i = 1 n f i x i where N = ∑ i = 1 n f i. In case of continuous frequency distribution, x i 's are the mid-values of the respective classes.

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Karl Pearson coefficient of skewness for grouped data

Details: Karl Pearson coefficient of skewness formula. The Karl Pearson’s coefficient skewness for grouped data is given by. Sk = Mean − Mode) sd = ¯ x − Mode sx. OR. Sk = 3(Mean − Median) sd = ¯ x − M sx. where, ¯ x is the sample mean, M is the median, sx is the sample standard deviation.

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Quartiles for ungrouped data - VrcAcademy

Details: Third Quartile Q3. The third quartile Q3 can be computed as follows: Q3 = Value of (3(n + 1) 4)th obs. = Value of (3(15 + 1) 4)th obs. = Value of (12)th obs. = 13 Thus, 75 % of the patients had length of stay in the hospital less than or equal to 13 days.

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Quartiles for grouped data - VrcAcademy

Details: Quartile for grouped data calculator. Use Quartile for grouped data calculator to find quartiles for grouped data based on type of frequency distributio (Discrete or Continuous),classes and frequencies of ith quartile class. It gives output as First Quartile,Second Quartile and Third Quartile.

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Percentiles for ungrouped data - VrcAcademy

Details: Percentiles for ungrouped data. Percentiles are the values of arranged data which divide whole data into hundred equal parts. They are 9 in numbers namely P 1, P 2, ⋯, P 99. Here P 1 is first percentile, P 2 is second percentile, P 3 is third percentile and so on.

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Gamma Distribution in Statistics - VrcAcademy

Details: Gamma Distribution. Gamma distribution is used to model a continuous random variable which takes positive values. Gamma distribution is widely used in science and engineering to model a skewed distribution. In this tutorial, we are going to discuss various important statistical properties of gamma distribution like graph of gamma distribution for various parameter combination, derivation of

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Capillary Rise Calculator - VrcAcademy

Details: Capillary Rise Calculator. Use below Capillary Rise Calculator equation calculates capillary rise in circular tube using surface tension,contact angle,liquid density,Gravitational Acceleration and tube radius.

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Quartile Deviation for grouped data - VrcAcademy

Details: The inter-quartile range is given by IQR = Q3 − Q1. using the quartile deviation formula for grouped data,formula for ith quartile is. Qi = (i(N) 4)th value, i = 1, 2, 3. where N is the total number of observations.

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Negative Binomial Distribution Examples - VrcAcademy

Details: The number of female children (successes) r = 2. Here X denote the number of male children before two female children. Then the random variable X follows a negative binomial distribution N B ( 2, 0.5). a. The probability distribution of X (number of male children before two female children) is.

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Confidence Interval for Difference of means (Dependent

Details: Confidence Interval for paired t-test. In this tutorial we will discuss how to determine confidence interval for the difference in means for dependent samples.

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Decile Calculator for Grouped Data with Examples - VrcAcademy

Details: Decile Calculator for grouped data. Use Decile calculator to find the Deciles for grouped data. Deciles for grouped data are the values which divide whole distribution in ten equal parts.These parts are 9 in numbers namely D1,D2..D9. here D1 refer first decile,D2 refer second decile and so on.

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Deciles for ungrouped data - VrcAcademy

Details: Deciles for ungrouped data. Deciles are the values of arranged data which divide whole data into ten equal parts. They are 9 in numbers namely D 1, D 2, ⋯, D 9. Here D 1 is first decile, D 2 is second decile, D 3 is third decile and so on.

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Normal Approximation to Binomial Distribution Calculator

Details: The general rule of thumb to use normal approximation to binomial distribution is that the sample size n is sufficiently large if n p ≥ 5 and n ( 1 − p) ≥ 5. For sufficiently large n, X ∼ N ( μ, σ 2). That is Z = X − μ σ = X − n p n p ( 1 − p) ∼ N ( 0, 1).

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Plasma Frequency Calculator - VrcAcademy

Details: Plasma Frequency Calculator. The frequency at which the plasma oscillation occurs is called the plasma frequency which can be calculated using this simple physics calculator based on electron number density, electronic charge, permittivity of vacuum and mass of electron.

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Variance and standard deviation for ungrouped data

Details: s x 2 = 1 n − 1 ∑ i = 1 n ( x i − x ¯) 2 = 1 n − 1 ( n ∑ i = 1 n x i 2 − ( ∑ i = 1 n x i) 2) The standard deviation of X is defined as the positive square root of variance. The standard deviation of X is given by. s x = s x 2. Below are the numerical examples with step by step guide solution on variance and standard deviation for

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Five number summary for grouped data - VrcAcademy

Details: Five number summary for grouped data. A five number summary is a quick and easy way to determine the the center, the spread and outliers (if any) of a data set. Five number summary includes five values, namely, minimum value ( min ), first quartile ( Q1 ), median ( Q2 ), third quartile ( Q3 ), maximum value ( max ).

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Geometric mean for grouped data - VrcAcademy

Details: Geometric mean for grouped data. Let ( x i, f i), i = 1, 2, ⋯, n be the given frequency distribution then the geometric mean of X is denoted by G M.

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Deciles for grouped data - VrcAcademy

Details: Deciles for grouped data. Deciles are the values of arranged data which divide whole data into ten equal parts. They are 9 in numbers namely D 1, D 2, ⋯, D 9. Here D 1 is first decile, D 2 is second decile, D 3 is third decile and so on.

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Discrete Uniform Distribution Calculator - VrcAcademy

Details: Step 1 - Enter the minumum value (a) Step 2 - Enter the maximum value (b) Step 3 - Enter the value of x. Step 4 - Click on “Calculate” for discrete uniform distribution. Step 5 - Calculate Probability. Step 6 - Calculate cumulative probabilities.

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Continuous Uniform Distribution Calculator - VrcAcademy

Details: Let the random variable X denote the weight of randomly chosen American passenger car. It is given that X ∼ U ( 2500, 4500). That is α = 2500 and β = 4500. using Continuous Uniform Distribution formula calculate probability density, mean of uniform distribution and variance of distribution.

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Negative Binomial Distribution Calculator - VrcAcademy

Details: Step 1 - Enter the number of successes (r) Step 2 - Enter the number of failures (x) Step 3 - Enter the probabilities of success (p) Step 4 - Click on “Calculate” for negative probability calculation. Step 5 - Calculate Probability. Step 6 - Calculate different cumulative probabilities.

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Quartiles for grouped data - VrcAcademy

Details: Quartiles. The formula for i t h quartile is. Q i = ( i ( N) 4) t h value, i = 1, 2, 3. where N is the total number of observations. First Quartile Q 1 can be calculated using quartile formula for grouped data as below. Q 1 = ( 1 ( N) 4) t h value = ( 1 ( 35) 4) t h value = ( 8.75) t h value.

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Cauchy Distribution in Statistics - VrcAcademy

Details: Cauchy Distribution. A continuous random variable X is said to follow Cauchy distribution with parameters μ and λ if its probability density function is given by f(x) = { λ π ⋅ 1 λ2 + ( x − μ)2, − ∞ < x < ∞; − ∞ < μ < ∞, λ > 0; 0, Otherwise. In notation it can be written as X ∼ C(μ, λ). The parameter μ and λ are

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Hypergeometric Distribution Examples - VrcAcademy

Details: Hypergeometric Experiment. In this tutorial, we will provide you step by step solution to some numerical examples on hypergeometric distribution to make sure you understand the hypergeometric distribution clearly and correctly.

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Percentiles for grouped data - VrcAcademy

Details: The formula for ith percentile is. Pi = (i(N) 100)th value, i = 1, 2, ⋯, 99. where N is the total number of observations. P30 = (30(N) 100)th value = (30(57) 100)th value = (17.1)th value The cumulative frequency just greater than or equal to 17.1 is 24, the corresponding class 19.5 − 30.5 is the 30th percentile class.

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Normal Approximation to Poisson Distribution - VrcAcademy

Details: Formula for continuity corrections. Poisson distribution is a discrete distribution, whereas normal distribution is a continuous distribution. When we are using the normal approximation to Poisson distribution we need to make correction while calculating various probabilities. P ( X = A) = P ( A − 0.5 < X < A + 0.5)

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Inter Quartile Range for grouped data - VrcAcademy

Details: First Quartile Q 1. Q 1 = ( 1 ( N) 4) t h value = ( 1 ( 35) 4) t h value = ( 8.75) t h value. The cumulative frequency just greater than or equal to 8.75 is 16. The corresponding value of X is the 1 s t quartile. That is, Q 1 = 3 days. Thus, 25 % of the students had absences less than or equal to 3 days.

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Geometric Distribution Examples in Statistics - VrcAcademy

Details: Geometric Distribution. In this tutorial, we will provide you step by step solution to some numerical examples on geometric distribution to make sure you understand the geometric distribution clearly and correctly.

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Mean Absolute Deviation for grouped data - VrcAcademy

Details: Mean absolute deviation for grouped data. Let ( x i, f i), i = 1, 2, ⋯, n be given frequency distribution. The mean of X is denoted by x ¯ and is given by. x ¯ = 1 N ∑ i = 1 n f i x i.

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Bernoulli Distribution in Statistics - VrcAcademy

Details: Introduction. In the theory of probability and statistics, a Bernoulli trial or Bernoulli Experiment is a random experiment with exactly two mutually exclusive outcomes, “Success” and “Failure” with the probability of success remains same every time the experiment is conducted. The name Bernoulli trial or Bernoulli distribution named after a Swiss scientist Jacob Bernoulli.

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Moment coefficient of kurtosis for ungrouped data - VrcAcademy

Details: Formula. The moment coefficient of kurtosis β 2 is defined as. β 2 = m 4 m 2 2. The moment coefficient of kurtosis γ 2 is defined as. γ 2 = β 2 − 3. where. n total number of observations. x ¯ sample mean. m 2 = 1 n ∑ i = 1 n ( x i − x ¯) 2 is second sample central moment.

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Variance and Standard Deviation for Grouped Data

Details: Step 3 - Sample standard deviation for grouped data. The standard deviation for grouped data is the positive square root of the variance. The sample standard deviation for grouped data calculated as. s x = s x 2 = 22.5 = 4.0734 days. Thus the standard deviation of total number of man days lost is 4.0734 days .

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Poisson Approximation to Binomial Distribution Calculator

Details: Poisson Approximation to Binomial Distribution. Let X be a binomially distributed random variable with number of trials n and probability of success p. The general rule of thumb to use Poisson approximation to binomial distribution is that the sample size n is sufficiently large and p is sufficiently small such that λ = n p (finite).

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Moment Coefficient of Skewness for ungrouped data - VrcAcademy

Details: Moment Coefficient of Skewness for ungrouped data. Moment Coefficient of Skewness is denoted by β 1 and is defined as. (1) β 1 = m 3 2 m 2 3. where m 2 and m 3 are second and third central moments. The gamma coefficient of skewness is defined as. (2) γ 1 = β 1 = m 3 m 2 3 / 2. If γ 1 > 0 or μ 3 > 0, then the data is positively skewed.

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Gamma Distribution Calculator - VrcAcademy

Details: Gamma Distribution Calculator. Gamma distribution is used to model a continuous random variable which takes positive values. Gamma distribution is widely used in science and engineering to model a skewed distribution. Use Gamma Distribution Calculator to find the probability density and lower and upper cumulative probabilities for Gamma distribution with parameter $\alpha$ and $\beta$.

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Binomial Distribution Calculator with Step by Step

Details: Step 2 - Enter the number of success (x) Step 3 - Enter the Probability of success (p) Step 4 - Click on Calculate button for binomial probabiity calculation. Step 5 - Calculate the mean of binomial distribution (np) Step 6 - Calculate the variance of binomial distribution np (1-p) Step 7 - Calculate Probability.

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Binomial Distribution Theory in Statistics - VrcAcademy

Details: Introduction. Binomial distribution is one of the most important discrete distribution in statistics. In this tutorial we will discuss about theory of Binomial distribution along with proof of some important results related to binomial distribution.

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Confidence Interval for Variance examples - VrcAcademy

Details: Example 2. The percentage rates of home ownership for 8 randomly selected states are listed below. Estimate the population variance and standard deviation for the percentage rate of home ownership with 99% confidence. 66.0, 75.8, 70.9, 73.9, 63.4, 68.5, 73.3, 65.9.

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Confidence Interval For Population Variance Calculator

Details: Step 5 Determine the confidence interval. 99 % confidence interval estimate for population variance is (n − 1)s2 χ2 ( α / 2, n − 1) ≤ σ2 ≤ (n − 1)s2 χ2 ( 1 − α / 2, n − 1) 7 ∗ 19.787 20.278 ≤ σ2 ≤ 7 ∗ 19.787 0.989 6.83 ≤ σ2 ≤ 140.049. Thus 99 % confidence interval for population variance is (6.83, 140.049).

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