What is the range of a measurement?

In the world of measurements, the range refers to the difference between the highest and lowest values observed. It's a simple way to express the spread or extent of a particular measurement. Think of it like the distance between the two ends of a measuring tape – it tells you how much space the measurement covers.

Here are some key points about the range:

  • Applicable to continuous data: The range is typically used for continuous data, where values can fall anywhere within a specific interval. It wouldn't be meaningful for categorical data like colors or types of fruits.
  • Easy to calculate: Calculating the range is straightforward. Simply subtract the lowest value from the highest value in your dataset.
  • Limitations: While easy to calculate, the range has limitations. It only considers the two extreme values and doesn't provide information about how the remaining data points are distributed within that range. It can be easily influenced by outliers (extreme values).

Here are some examples of how the range is used:

  • Temperature: The range of temperature in a city over a month might be calculated as the difference between the highest and lowest recorded temperatures.
  • Test scores: The range of scores on an exam could be the difference between the highest and lowest score achieved by students.
  • Product dimensions: The range of sizes for a particular type of clothing could be the difference between the smallest and largest sizes available.

While the range offers a basic understanding of the spread of data, other measures like the interquartile range (IQR) and standard deviation provide more nuanced information about the distribution and variability within the data.

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Supporting content
What is a standard deviation?

What is a standard deviation?

A standard deviation (SD) is a statistical measure that quantifies the amount of variation or spread of data points around the mean (average) in a dataset. It expresses how much, on average, each data point deviates from the mean, providing a more informative understanding of data dispersion compared to the simple range.

Formula of the standard deviation:

\[ s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} . \]

where:

  • s represents the
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