# What is variability in Statistics

What is Variability in Statistics? In a nutshell, It’s statistics that represent the amount of dispersion in data or spread of a data set. While a measure of central tendency describes the typical value, they define how far away the data points tend to fall from the center. A low dispersion shows that the data points tend to be clustered tightly around the center. High dispersion indicates that they tend to fall further away.

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## What is Variability Statistics

In statistics, dispersion, variability, and spread are synonyms that denote the width of the distribution. Just as there are various measures of central tendency, there are several measures of variability. Here, you’ll l get to understand why the variability of your data is critical. Then, explore the most common measures of variability that is the range, interquartile range, variance, and standard deviation.

## Why Understanding Variability is Important.

Analysts often use the mean to summarize the center of a population or a process. While the mean is important, people often react to variability even more. When a distribution has lower variability, the values in a dataset are more reliable. Nevertheless, when the variability is higher, the data points are more unlike and extreme values become more likely. Consequently, understanding variability helps you know the likelihood of unusual events.

Some variation is inevitable, but problems occur at the extremes. Distributions with greater variability produce observations with unusually large and small values more frequently than distributions with less variability.

## Range

The range of a dataset is the difference between the largest and smallest values in that dataset. For example, in the two datasets below, dataset 1 has a range of 20 – 38 = 18 while dataset 2 has a range of 11 – 52 = 41. Dataset 2 has a broader range and, hence, more variability than dataset 1.

While the range is easy to understand, it is based on only the two most extreme values in the dataset, which makes it very susceptible to outliers. If one of those numbers is unusually high or low, it affects the entire range even if it is atypical.

Additionally, the size of the dataset affects the range. In general, you are less likely to observe extreme values. However, as you increase the sample size, you have more opportunities to obtain these extreme values. Consequently, when you draw random samples from the same population, the range tends to increase as the sample size increases. Consequently, use the range to compare variability only when the sample sizes are similar.

## The Interquartile Range (IQR)

The interquartile range is the middle half of the data. To visualize it, think about the median value that splits the dataset in half. Similarly, you can divide the data into quarters. Statisticians refer to these quarters as quartiles and denote them from low to high as Q1, Q2, and Q3. The lowest quartile (Q1) contains the quarter of the dataset with the smallest values. The upper quartile (Q4) contains the quarter of the dataset with the highest values. The interquartile range is the middle half of the data that is in between the upper and lower quartiles. In other words, the interquartile range includes 50% of data points that fall between Q1 and Q3. The IQR is the red area in the graph below.

The interquartile range is a robust measure of variability similarly that the median is a robust measure of central tendency. Neither measure is influenced dramatically by outliers because they don’t depend on every value. Additionally, the interquartile range is excellent for skewed distributions, just like the median. When you have a normal distribution, the standard deviation tells you the percentage of observations that fall specific distances from the mean. However, this doesn’t work for skewed distributions, and the Interquartile range is a great alternative.

## Variance

Variance is the average squared difference of the values from the mean. Unlike the previous measures of variability, the variance includes all values in the calculation by comparing each value to the mean. To calculate this statistic, you calculate a set of squared differences between the data points and the mean, sum them, and then divide by the number of observations. Hence, it’s the average squared difference.

## Standard Deviation

The standard deviation is the standard or typical difference between each data point and the mean. When the values in a dataset are grouped closer together, you have a smaller standard deviation. On the other hand, when the values are spread out more, the standard deviation is larger because the standard distance is greater.

Conveniently, the standard deviation uses the original units of the data, which makes interpretation easier. The standard deviation is just the square root of the variance

The standard deviation is similar to the mean absolute deviation. Both use the original data units and they compare the data values to the mean to assess variability

People often confuse the standard deviation with the standard error of the mean. Both measures assess variability, but they have extremely different purposes.

## Which is Best—the Range, Interquartile Range, or Standard Deviation?

When you are comparing samples that are the same size, consider using the range as the measure of variability. It’s a reasonably intuitive statistic. Just be aware that a single outlier can throw the range off. The range is particularly suitable for small samples when you don’t have enough data to calculate the other measures reliably, and the likelihood of obtaining an outlier is also lower.

When you have a skewed distribution, the median is a better measure of central tendency, and it makes sense to pair it with either the interquartile range or other percentile-based ranges because all of these statistics divide the dataset into groups with specific proportions.

For normally distributed data or even data that aren’t skewed, using the tried and true combination of reporting the mean and the standard deviation is the way to go. This combination is by far the most common. You can still supplement this approach with percentile-based ranges as you need.

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