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Statistics By Jim

Making statistics intuitive

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Box Plot Explained with Examples

By Jim Frost Leave a Comment

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

Filed Under: Graphs Tagged With: choosing analysis, data types, distributions, graphs

Unimodal Distribution Definition & Examples

By Jim Frost Leave a Comment

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

Filed Under: Basics Tagged With: conceptual, distributions, graphs

Random Variable: Discrete & Continuous

By Jim Frost Leave a Comment

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

Filed Under: Probability Tagged With: analysis example, conceptual, distributions, graphs

Least Squares Regression: Definition, Formulas & Example

By Jim Frost 1 Comment

A least squares regression line represents the relationship between variables in a scatterplot. The procedure fits the line to the data points in a way that minimizes the sum of the squared vertical distances between the line and the points. It is also known as a line of best fit or a trend line. [Read more…] about Least Squares Regression: Definition, Formulas & Example

Filed Under: Regression Tagged With: analysis example, graphs, interpreting results

Probability Mass Function: Definition, Uses & Example

By Jim Frost Leave a Comment

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

Filed Under: Probability Tagged With: distributions, graphs

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

By Jim Frost Leave a Comment

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

Filed Under: Probability Tagged With: analysis example, conceptual, distributions, graphs, interpreting results

Slope Intercept Form of Linear Equations: A Guide

By Jim Frost Leave a Comment

What is Slope Intercept Form?

The slope intercept form of linear equations is an algebraic representation of straight lines: y = mx + b. [Read more…] about Slope Intercept Form of Linear Equations: A Guide

Filed Under: Basics Tagged With: analysis example, graphs, interpreting results

Hypergeometric Distribution: Uses, Calculator & Formula

By Jim Frost Leave a Comment

What is a Hypergeometric Distribution?

The hypergeometric distribution is a discrete probability distribution that calculates the likelihood an event happens k times in n trials when you are sampling from a small population without replacement. [Read more…] about Hypergeometric Distribution: Uses, Calculator & Formula

Filed Under: Probability Tagged With: distributions, graphs

Negative Binomial Distribution: Uses, Calculator & Formula

By Jim Frost Leave a Comment

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

Filed Under: Probability Tagged With: conceptual, distributions, graphs

Benford’s Law Explained with Examples

By Jim Frost Leave a Comment

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

Filed Under: Probability Tagged With: distributions, Excel, graphs

Probability Density Function: Definition & Uses

By Jim Frost 12 Comments

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

Filed Under: Probability Tagged With: conceptual, distributions, graphs

T Distribution: Definition & Uses

By Jim Frost Leave a Comment

What is the T Distribution?

The t distribution is a continuous probability distribution that is symmetric and bell-shaped like the normal distribution but with a shorter peak and thicker tails. It was designed to factor in the greater uncertainty associated with small sample sizes.

The t distribution describes the variability of the distances between sample means and the population mean when the population standard deviation is unknown and the data approximately follow the normal distribution. This distribution has only one parameter, the degrees of freedom, based on (but not equal to) the sample size. [Read more…] about T Distribution: Definition & Uses

Filed Under: Probability Tagged With: conceptual, distributions, graphs

Difference Between Standard Deviation and Standard Error

By Jim Frost 6 Comments

The difference between a standard deviation and a standard error can seem murky. Let’s clear that up in this post!

Standard deviation (SD) and standard error (SE) both measure variability. High values of either statistic indicate more dispersion. However, that’s where the similarities end. The standard deviation is not the same as the standard error. [Read more…] about Difference Between Standard Deviation and Standard Error

Filed Under: Basics Tagged With: conceptual, distributions, graphs

Beta Distribution: Uses, Parameters & Examples

By Jim Frost 6 Comments

The beta distribution is a continuous probability distribution that models random variables with values falling inside a finite interval. Use it to model subject areas with both an upper and lower bound for possible values. Analysts commonly use it to model the time to complete a task, the distribution of order statistics, and the prior distribution for binomial proportions in Bayesian analysis. [Read more…] about Beta Distribution: Uses, Parameters & Examples

Filed Under: Probability Tagged With: conceptual, distributions, graphs

Geometric Distribution: Uses, Calculator & Formula

By Jim Frost Leave a Comment

What is a Geometric Distribution?

The geometric distribution is a discrete probability distribution that calculates the probability of the first success occurring during a specific trial. In other words, during a series of attempts, what is the probability of success first occurring during each attempt? Use this distribution when you need to understand how many attempts are necessary to produce the first successful outcome. [Read more…] about Geometric Distribution: Uses, Calculator & Formula

Filed Under: Probability Tagged With: distributions, graphs

Bimodal Distribution: Definition, Examples & Analysis

By Jim Frost 1 Comment

A bimodal distribution has two peaks. In the context of a continuous probability distribution, modes are peaks in the distribution. The graph below shows a bimodal distribution. [Read more…] about Bimodal Distribution: Definition, Examples & Analysis

Filed Under: Basics Tagged With: conceptual, distributions, graphs

Binomial Distribution: Uses, Calculator & Formula

By Jim Frost 2 Comments

What is a Binomial Distribution?

The binomial distribution is a discrete probability distribution that calculates the likelihood an event will occur a specific number of times in a set number of opportunities. Use this distribution when you have a binomial random variable. These variables count how often an event occurs within a fixed number of trials. They have only two possible outcomes that are mutually exclusive. [Read more…] about Binomial Distribution: Uses, Calculator & Formula

Filed Under: Probability Tagged With: distributions, graphs

F-table

By Jim Frost Leave a Comment

These F-tables provide the critical values for right-tail F-tests. Your F-test results are statistically significant when its test statistic is greater than this value. [Read more…] about F-table

Filed Under: Hypothesis Testing Tagged With: conceptual, distributions, graphs

Sampling Distribution: Definition, Formula & Examples

By Jim Frost 5 Comments

What is a Sampling Distribution?

A sampling distribution of a statistic is a type of probability distribution created by drawing many random samples of a given size from the same population. These distributions help you understand how a sample statistic varies from sample to sample. [Read more…] about Sampling Distribution: Definition, Formula & Examples

Filed Under: Hypothesis Testing Tagged With: conceptual, distributions, graphs

Critical Value: Definition, Finding & Calculator

By Jim Frost Leave a Comment

What is a Critical Value?

A critical value defines regions in the sampling distribution of a test statistic. These values play a role in both hypothesis tests and confidence intervals. In hypothesis tests, critical values determine whether the results are statistically significant. For confidence intervals, they help calculate the upper and lower limits. [Read more…] about Critical Value: Definition, Finding & Calculator

Filed Under: Hypothesis Testing Tagged With: conceptual, distributions, graphs

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    Top Posts

    • How to Interpret P-values and Coefficients in Regression Analysis
    • How To Interpret R-squared in Regression Analysis
    • Mean, Median, and Mode: Measures of Central Tendency
    • F-table
    • Z-table
    • Multicollinearity in Regression Analysis: Problems, Detection, and Solutions
    • Purposive Sampling: Definition & Examples
    • How to do t-Tests in Excel
    • T-Distribution Table of Critical Values
    • Interpreting Correlation Coefficients

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