Statistics By Jim

Making statistics intuitive

distributions

Median Absolute Deviation: Definition, Finding & Formula

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What is the Median Absolute Deviation?

The median absolute deviation is a measure of variability that indicates the typical distance between observations and the median. Unlike the mean absolute deviation, which uses the average, this method centers on the median, making it more resistant to outliers. The result uses the same units as the data, which helps with interpretation. Larger values signify that the data points spread further from the median, while lower values mean they cluster more tightly around it. Statisticians frequently abbreviate it as MAD, but sometimes use MADM to avoid confusion with the mean absolute deviation. [Read more…] about Median Absolute Deviation: Definition, Finding & Formula

Binomial Distribution Formula: Probability, Standard Deviation & Mean

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Binomial Distribution Formula

Use the binomial distribution formula to calculate the likelihood an event will occur a specific number of times in a set number of opportunities. I’ll show you the binomial distribution formula to calculate these probabilities manually.

In this post, I’ll walk you through the formulas for how to find the probability, mean, and standard deviation of the binomial distribution and provide worked examples. [Read more…] about Binomial Distribution Formula: Probability, Standard Deviation & Mean

Expected Value: Definition, Formula & Finding

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What is the Expected Value?

The expected value in statistics is the long-run average outcome of a random variable based on its possible outcomes and their respective probabilities. Essentially, if an experiment (like a game of chance) were repeated, the expected value tells us the average result we’d see in the long run. Statisticians denote it as E(X), where E is “expected value,” and X is the random variable. [Read more…] about Expected Value: Definition, Formula & Finding

Bernoulli Distribution: Uses, Formula & Example

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What is the Bernoulli Distribution?

The Bernoulli distribution is a discrete probability distribution that models a binary outcome for one trial. Use it for a random variable that can take one of two outcomes: success (k = 1) or failure (k = 0), much like a coin toss. Statisticians refer to these trials as Bernoulli trials. [Read more…] about Bernoulli Distribution: Uses, Formula & Example

Kruskal Wallis Test Explained

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What is the Kruskal Wallis Test?

The Kruskal Wallis test is a nonparametric hypothesis test that compares three or more independent groups. Statisticians also refer to it as one-way ANOVA on ranks. This analysis extends the Mann Whitney U nonparametric test that can compare only two groups. [Read more…] about Kruskal Wallis Test Explained

Mann Whitney U Test Explained

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What is the Mann Whitney U Test?

The Mann Whitney U test is a nonparametric hypothesis test that compares two independent groups. Statisticians also refer to it as the Wilcoxon rank sum test. The Kruskal Wallis test extends this analysis so that can compare more than two groups. [Read more…] about Mann Whitney U Test Explained

Box Plot Explained with Examples

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What is a Box Plot?

A box plot, sometimes called a box and whisker plot, provides a snapshot of your continuous variable’s distribution. They particularly excel at comparing the distributions of groups within your dataset. A box plot displays a ton of information in a simplified format. Analysts frequently use them during exploratory data analysis because they display your dataset’s central tendency, skewness, and spread, as well as highlighting outliers. [Read more…] about Box Plot Explained with Examples

Trimmed Mean: Definition, Calculating & Benefits

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What is a Trimmed Mean?

The trimmed mean is a statistical measure that calculates a dataset’s average after removing a certain percentage of extreme values from both ends of the distribution. By excluding outliers, this statistic can provide a more accurate representation of a dataset’s typical or central values. Usually, you’ll trim a percentage of values, such as 10% or 20%. [Read more…] about Trimmed Mean: Definition, Calculating & Benefits

Unimodal Distribution Definition & Examples

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What is a Unimodal Distribution?

A unimodal distribution in statistics refers to a frequency distribution that has only one peak. Unimodality means that a single value in the distribution occurs more frequently than any other value. The peak represents the most common value, also known as the mode. [Read more…] about Unimodal Distribution Definition & Examples

Random Variable: Discrete & Continuous

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What is a Random Variable?

A random variable is a variable where chance determines its value. They can take on either discrete or continuous values, and understanding the properties of each type is essential in many statistical applications. Random variables are a key concept in statistics and probability theory. [Read more…] about Random Variable: Discrete & Continuous

Probability Mass Function: Definition, Uses & Example

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What is a Probability Mass Function?

A probability mass function (PMF) is a mathematical function that calculates the probability a discrete random variable will be a specific value. PMFs also describe the probability distribution for the full range of values for a discrete variable. A discrete random variable can take on a finite or countably infinite number of possible values, such as the number of heads in a series of coin flips or the number of customers who visit a store on a given day. [Read more…] about Probability Mass Function: Definition, Uses & Example

Cumulative Distribution Function (CDF): Uses, Graphs & vs PDF

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What is a Cumulative Distribution Function?

A cumulative distribution function (CDF) describes the probabilities of a random variable having values less than or equal to x. It is a cumulative function because it sums the total likelihood up to that point. Its output always ranges between 0 and 1. [Read more…] about Cumulative Distribution Function (CDF): Uses, Graphs & vs PDF

Monte Carlo Simulation: Make Better Decisions

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What is Monte Carlo Simulation?

Monte Carlo simulation uses random sampling to produce simulated outcomes of a process or system. This method uses random sampling to generate simulated input data and enters them into a mathematical model that describes the system. The simulation produces a distribution of outcomes that analysts can use to derive probabilities. [Read more…] about Monte Carlo Simulation: Make Better Decisions

Negative Binomial Distribution: Uses, Calculator & Formula

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What is a Negative Binomial Distribution?

The negative binomial distribution describes the number of trials required to generate an event a particular number of times. When you provide an event probability and the number of successes (r), this distribution calculates the likelihood of observing the Rth success on the Nth attempt. Statisticians also refer to this discrete probability distribution as the Pascal distribution. [Read more…] about Negative Binomial Distribution: Uses, Calculator & Formula

Benford’s Law Explained with Examples

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What is Benford’s Law?

Benford’s law describes the relative frequency distribution for leading digits of numbers in datasets. Leading digits with smaller values occur more frequently than larger values. This law states that approximately 30% of numbers start with a 1 while less than 5% start with a 9. According to this law, leading 1s appear 6.5 times as often as leading 9s! Benford’s law is also known as the First Digit Law. [Read more…] about Benford’s Law Explained with Examples

Probability Density Function: Definition & Uses

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What is a Probability Density Function (PDF)?

A probability density function describes a probability distribution for a random, continuous variable. Use a probability density function to find the chances that the value of a random variable will occur within a range of values that you specify. More specifically, a PDF is a function where its integral for an interval provides the probability of a value occurring in that interval. For example, what are the chances that the next IQ score you measure will fall between 120 and 140? In statistics, PDF stands for probability density function. [Read more…] about Probability Density Function: Definition & Uses