# Free Statistics Calculators Online

See below for a list of our ever-growing number statistics calculators. First let’s start with the basics and then we’ll get to some of our more complex calculators.

## Mean

The mean is the average of a set of numbers and is one of the most foundational calculations done in all of statistics. To use our mean calculator simply paste in all of your numbers into the form field, separate them by a comma, and click calculate. That’s pretty much all you need to know.

Formula:

μ = Σx/n

Where:

- Σ represents summation (the sum of all)
- x is the set of values
- n is the total number of values.

## The Mode

The mode in statistics refers to the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. The mode can be used to identify the most common or frequent occurrence of a characteristic or value in a data set. For instance, in a clothing store that sells items in various sizes, the mode can help identify the most popular size, thereby informing the inventory decisions of the store.

The mode is particularly useful when dealing with non-numerical data, as it can be applied to any data type. It also remains unaffected by extreme values in the data set, unlike the mean. In fields like market research or opinion polling, where the most frequent response or characteristic is often of great interest, the mode can provide valuable insights.

How to find the Mode (other than using our calculator):

- Order your data from smallest to largest.
- If n is odd, the median is the ((n + 1) / 2)th value.
- If n is even, the median is the average of the (n / 2)th and ((n / 2) + 1)th values.

## Median Calculator

The median in statistics is the middle value in a data set when the values are arranged in ascending or descending order. If there is an even number of observations, the median is the average of the two middle numbers. The median is a very useful measure of central tendency when dealing with skewed distributions because it isn’t affected by extreme values.

In terms of use cases, the median is often used in income and property value studies, as these fields often involve large data sets with high variability and potentially extreme outliers. For instance, a handful of extremely high incomes can significantly skew the mean, making it a less accurate representation of a typical income. The median, on the other hand, would not be skewed by these high incomes, providing a more accurate picture of what a ‘typical’ income might be. Similarly, in real estate, the median home price is often reported, as it provides a more accurate picture of the typical home price in a certain area, ignoring a few unusually high or low prices. Try our simple online median calculator.

## Random Number Generator

Use our Random Number generator tool free online. Simply put in a minimum number and a maximum number and the calculator will print a random number between these two numbers.

For example if you were to input minimum 1, maximum 10 and click “generate” the random number generator might output “5.” Use cases include doing free giveaways or trying to settle a score in a free and unbiased way.

## Representative Sample Calculator

One of the most important concepts in statistics, the **representative sample** in statistics is a subset of a statistical population that accurately reflects the characteristics of the whole population. The concept of a representative sample is essential in the field of statistics because it allows for accurate predictions and conclusions about larger groups based on studying a smaller, more manageable subset. The aim is to select a sample that has the same distribution of characteristics as the entire population. Try our free representative sample calculator or read more about use cases.

In terms of practical use, representative samples are incredibly important in survey data collection and observational studies across numerous fields. For example, in political polling, a representative sample of voters can give an indication of how the entire population might vote. Similarly, in medical research, a representative sample of patients can help in understanding the probable effects of a drug in the broader patient population. The key is that the sample should accurately reflect the larger population’s demographic and characteristic distribution.

## Quartile Calculator

In statistics, quartiles are values that divide a data set into four equal parts. The first quartile (Q1) is the median of the lower half of the data, the second quartile (Q2) is the median of the whole data set, and the third quartile (Q3) is the median of the upper half of the data. Quartiles are used to calculate the interquartile range, which is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles.

In terms of applications, quartiles are used in descriptive statistics to give a quick snapshot of the distribution of a data set. They are particularly useful in identifying outliers and understanding the spread of your data. For example, in finance, quartiles can help to understand the distribution of income or wealth within a population. In a business setting, quartiles could be used to analyze sales data, customer feedback scores, or website traffic data. In all these cases, quartiles provide an easy way to understand the dispersion and skewness of the data. Ready to try yourself? Use our online Quartile Calculator.

## Standard Deviation Calculator

This Standard Deviation Calculator is a simple tool that allows you to calculate the standard deviation of a data set with ease. Standard deviation, a fundamental concept in statistics, measures the amount of variation or dispersion in a dataset. This calculator eliminates the need for manual calculations and provides a quick, accurate measure of your data’s dispersion. Whether you’re analyzing financial data, health data, social science research, or even weather patterns, this calculator is an essential tool to help you understand the variability in your data set.

Where:

- σ is the standard deviation
- xi are the observed values in the sample
- μ is the mean of the sample
- N is the number of observations in the sample

Please note that the above formula represents the calculation of standard deviation for a population. If you are calculating the standard deviation for a sample, you would divide by (N – 1) instead of N in the third step, which is known as Bessel’s correction. This correction is used to correct the bias in the estimation of the population variance. However, if your sample size is large, this distinction becomes less important.

## Randomly Select Winner From List of Emails

Running a contest giveaway and need a fair way to select a winner from a list of emails? Use our free online tool which allows you to quickly, fairly and privately randomly select a winner from a list of emails.

Simply paste in your comma separated emails into the form field and click the button ‘Select Winner.’ Note no emails that you enter into the form field will be saved on our end.