Explain How To Find The Range Of A Data Set

The range of a data set is the divergence between the maximum and the minimum values. Information technology measures variability using the same units as the data. Larger values stand for greater variability.

The range is the easiest measure of dispersion to calculate and translate in statistics, but it has some limitations. In this post, I'll show you how to find the range mathematically and graphically, interpret information technology, explain its limitations, and clarify when to use it.

Formula

To observe the range in statistics, take the largest value and decrease the smallest value from it.

Range = Highest value – Lowest value

It cannot exist a negative value because the formula takes the larger value and subtracts the smaller value.

Related post: Measures of Variability

Example of Finding the Range

For example, in the worksheet below, Dataset one has a range of 38 – 20 = 18, while for Dataset ii it is 52 – eleven = 41. Dataset 2 has a broader range and, therefore, is more variable than Dataset i.

Conveniently, you tin can find the minimum, maximum, and range values in the descriptive statistics output from statistical software. Excel's Descriptive Statistics function includes them, as shown below.

Related post: Descriptive Statistics in Excel

Finding the Range in Graphs

You can find data ranges in several types of graphs, including histograms, boxplots, and scatterplots. In the instance graphs beneath, the red lines correspond the ranges. The following graphical representations bring the concept to life. If yous're looking at a chart and don't have the data, you'll take to approximate the values visually.

Histograms

In a histogram, the range is the width that the bars cover along the x-centrality. These are approximate values considering histograms brandish bin values rather than raw data values.

In these histograms, distribution A has an guess range of 65 – 40 = 25 and for distribution C it is ninety – 20 = seventy. Distribution C has a broader spread, and its extensive width in the graph illustrates this property.

Boxplots

Boxplots brandish data ranges for groups inside a dataset. In boxplots, it equals the entire length of the whiskers for each group. The minimum and maximum values appear at the ends of the whiskers except when in that location are outliers. Consequently, ranges in boxplots exclude outliers.

In this boxplot, the scores for Method 3 spread from approximately 37 to 12, producing a range of 25. This group has the largest spread in the dataset. Conversely, Method 2 has the smallest spread of thirty – 20 = 10. Method 2 has an outlier (the asterisk), but the boxplot conveniently excludes it.

Scatterplots

In scatterplots, you tin discover the range of two variables at one fourth dimension. For the y-axis variable, it is the elevation of the data, while it'southward the width for the 10-axis variable.

This scatterplot displays the superlative and weights of preteen girls in a inquiry study. For these data, weight has a range of approximately 90 – 31 = 59 kilograms and for elevation it is 1.67 – 1.33 = 0.34 meters.

Note:  When you're assessing mathematical functions rather than data values, the range of f(x) appears on the y-axis (outputs), and the domain is on the 10-axis (inputs).

Related posts: Histograms, Boxplots, and Scatterplots

Limitations of Using the Range

The range is simple to sympathize merely it has some limitations you need to consider.

Unfortunately, outliers tin can influence information technology considerably because it uses only the 2 most extreme values. If ane value in the dataset is atypically low or high, it changes the unabridged range all by itself.

Allow's return to the first two data sets in this post. However, I've changed the lesser number in Dataset 1 from xviii to 102. The new spread is 82. The single change caused it to increment from 18 to 82. Co-ordinate to the new value, Dataset 1 appears to have more variability than Dataset 2 (r = 41). However, all values except the ane outlier in Dataset 1 autumn between twenty and 34.

The range is not a robust statistic. The standard deviation and, particularly, the interquartile range are more robust to outliers.

Related postal service: What are Robust Statistics?

Additionally, the sample size itself influences this statistic. As the sample size grows, the range tends to increment. Consequently, you can't compare values between samples of unlike sizes.

Why does this happen? Overall, extreme values have lower probabilities of occurring. However, equally the sample size increases, extreme values have more opportunities to appear. Consequently, the range tends to spread as the sample size increases.

If you need to compare the variability of unlike size datasets, use another measure out, such equally the standard divergence.

When to Utilize the Range?

Taking the weaknesses into consideration, when is the range a skilful measure of variability?

It tin be an splendid measure when you need an intuitive statistic that indicates the degree to which the data are spread out. Everyone can understand the concept of the departure between the maximum and minimum data points. It's likewise like shooting fish in a barrel to summate in your head using summary statistics when you demand a quick assessment.

Use the range with small datasets to avert outliers and when you're comparing samples of the same size.

It's also a peachy statistic for detecting information entry errors. Because it is and then susceptible to outliers, a single mistake can manifest itself. You're taking a weakness and using it for something positive! For example, if yous find that the range of people'south peak in a sample is two meters, at that place's an error!

Using It for Quality Control

Quality control analysts oft use this item measure of variability. For starters, if the range for a batch of products is larger than the spread of the upper and lower spec limits, they know that at least one office is out of spec!

For instance, if the range of office lengths is 5mm, but the spread for the spec limits is 3mm, at that place must be parts out of spec.

Quality control analysts also use R charts, which are range charts—a type of control chart. These graphs monitor the variation in a process by tracking the range over time. They use R charts with small (northward = two–x), consistently sized batches of a product from a stable process, which avoids the pitfalls I mentioned before. These graphs quickly detect unstable variability in the process.

In an R chart, the data points represent the ranges for samples taken over time. When a sample value crosses the control limits (ruddy lines), the procedure is out of statistical control. This process is in control.

Related postal service: Using Command Charts with Hypothesis Tests

Source: https://statisticsbyjim.com/basics/range/

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