# Variation

## What Is Variation

In statistics, **variation** is the differences in measurements or observations. These differences can be caused by many factors, including measurement error, randomness, or the underlying distribution of the data.

Variation can be measured in several ways, including the range, standard deviation, and variance. The range is the simplest measure of variation and is simply the difference between the largest and smallest values in a data set. The standard deviation is a more sophisticated measure that takes into account how far each value is from the mean (average) of the data set. The variance is a slightly different way of measuring variation that is used mainly by statisticians.

The amount of variation in a data set affects both the level of accuracy and precision of measurements made from that data set. For example, if the variation in a data set is large, then individual measurements are less likely to be accurate. On the other hand, if the variation is small, then individual measurements are more likely to be precise.

There are many sources of variation in data sets, including measurement error, randomness, and the underlying distribution of the data.

Measurement error is the error that occurs when a value is measured incorrectly. This type of error can occur for many reasons, including incorrect use of measuring instruments or human error.

Randomness is another source of variation and occurs when the data values are randomly distributed. This type of variation cannot be predicted or controlled.

The underlying distribution of the data is the final source of variation and refers to the way in which the data values are distributed. This type of variation can be due to many factors, including the nature of the measuring process, the population being measured, or the sampling method used.

Variation is an important concept in statistics because it affects both the level of accuracy and precision of measurements. It is important to understand the sources of variation in order to properly interpret data sets.

### What Are the Two Types of Variation in Statistics

Common Cause Variation

Special Cause Variation

**Common Cause Variation**

Common cause variation is caused by factors that are in the process itself. These factors can't be controlled, and they result in normal fluctuations in process output. Common causes are often due to the nature of the process material, tools, or equipment. For example, common causes of variation in a manufacturing process might include changes in temperature or humidity.

**Special Cause Variation**

Special cause variation is due to factors that can be identified and controlled. These variations are not due to the inherent nature of the process but rather to specific events that occur during production. Special causes of variation include machine downtime, operator error, or a change in the raw materials used in production. identifying and eliminating special causes of variation is essential to improving process performance.

Both types of variation can significantly impact the quality of the products or services produced by a business. It's important to be aware of both types of variation and take steps to minimize their effects on process performance.

Monitoring process performance can help to identify both common and special causes of variation. Statistical tools such as control charts can track process performance over time and identify when variation falls outside the normal range. Businesses can improve quality and efficiency by identifying and eliminating special causes of variation.

## What Are the Three Measures of Variation

Variation is a measure of how spread out data is. It can be measured in terms of the range, variance, and standard deviation.

The range is the difference between the largest and smallest values in a data set. The variance is a measure of how much each value in a data set differs from the mean. The standard deviation is a measure of how much each value in a data set differs from the mean.

**Range:** The range is the difference between a data set's largest and smallest values. Simply subtract the minimum value from the maximum value to calculate the range.

**Variance:** The variance is a measure of how much each value in a data set differs from the mean. To calculate the variance, take the sum of the squares of the differences between each value and the mean and then divide by the number of values.

**Standard Deviation:** The standard deviation is a measure of how much each value in a data set differs from the mean. To calculate the standard deviation, take the square root of the variance.

The range, variance, and standard deviation are all measures of variation. The range is the simplest measure of variation, and the standard deviation is the most common measure of variation. The variance is a more sophisticated measure of variation but is not as commonly used as the other two measures.

There are many reasons why data sets may vary in terms of their statistics. Some data sets may have more extreme values than others. Some data sets may be more spread out than others. And some data sets may have more variation in their means than others.

Variation is a normal and expected part of data sets. It is not always a bad thing, and it is not always a good thing. It all depends on the context of the data set and what you are trying to accomplish with the data.

If you are looking for outliers in a data set, then you want to look for data sets with high variation. If you are trying to find the average value of a data set, then you want to look for data sets with low variation. And if you are trying to create a model of a data set, then you want to look for data sets with a moderate variation.

Variation is an important concept in statistics, and it is one that you should be familiar with. It is a normal part of data sets, and it is something that you will encounter often. So, take some time to learn about variation and how it can impact your data sets.

## Why Is Variation Important in Statistics

In statistics, variation is important because it allows us to measure the dispersion of data points around a central tendency. This dispersion can be measured in terms of the standard deviation or variance. Variation is also important because it allows us to identify outliers in our data set.