The difference between the highest and lowest observation could also be characterized as the range. The range of the observation is the term that is used to describe the outcome. In statistics, the range denotes the dispersion of observations.

The difference between the largest value and the smallest values in a set of data is known as the range in statistics. The difference here is that the range of a collection of data is calculated by subtracting the sample maximum and minimum value.

DISPERSION: –

Dispersion is the state of being dispersed or spread out. The extent to which numerical data is likely to vary around an average value is referred to as statistical dispersion. In other words, dispersion aids in the comprehension of data distribution.

Measure of dispersion: –

Measures of dispersion are used in statistics to interpret data variability, i.e. to determine how homogeneous or heterogeneous the data is. In simple words, it indicates whether the variable is squeezed or distributed.

Generally, there are two methods by which we can measure the dispersion of the data i.e.

  • The Absolute measure of dispersion
  • The relative measure of dispersion

Absolute measure of dispersion: –

An absolute measure of dispersion consists of the same unit as the original data set is used in an absolute measure of dispersion. The absolute dispersion approach expresses changes as the average of observed deviations, such as standard or mean deviations. It includes terms such as range, standard deviation, and quartile deviation, among others.

Some of the types of absolute measure of dispersion are: –

  1. Range: – The difference between the highest and lowest observation could also be characterized as the range. The range of the observation is the term that is used to describe the outcome.
  2. Variance: – The variance is calculated by subtracting the mean from each data point in the set, then squaring and adding each square, and lastly dividing them by the total number of the values in the data set.
  3. Standard deviation: – the square root of the variance is known as standard deviation.
  4. Mean and mean deviation: – The mean is the arithmetic mean of the absolute deviations of the observations from a measure of central tendency, and the mean deviation is the arithmetic mean of the absolute deviations of the data from a measure of central tendency (also called mean absolute deviation).

Relative measure of dispersion

When comparing the distribution of two or more data sets, relative measures of dispersion are used. This metric compares values without the use of units. The following are some examples of common relative dispersion methods:

  1. Coefficient of Range
  2. Coefficient of Variation
  3. Coefficient of Standard Deviation
  4. Coefficient of Quartile Deviation
  5. Coefficient of Mean Deviation

Range of data

The range of the data in statistics is the range from the lowest to the highest value in the distribution. It’s a common statistic for determining variability. Measures of variability, like measures of central tendency, provide descriptive statistics for describing the data collection. The range is calculated by subtracting the lowest from the highest value. In a distribution, a large range suggests high variability, while a short range indicates low variability.

Measure of range

There are only two steps by which we can measure the range of any data or observation i.e.

  • From low to high, sort all of the values in the given data set.

          Write down all of the figures you’d like to calculate from your data set. After you’ve gathered all of your numbers, sort them from lowest to highest. This gives you a better idea of how your values differ from one another and makes finding the lowest and greatest numbers in your collection easier.

  • Now subtracting the lowest value from highest value

              We can readily find the lowest and largest numbers in the equation now that our numbers are in ascending order. These two values are the most significant parts of the formula because they help us understand how the numbers in the data set differ.

And then we get the range of the data.

Range = Highest Value – Lowest Value

Or, Range = Highest observation – Lowest observation

CONCLUSION: –

When you have a distribution with no extreme values, the range is an excellent indicator of variability. When used with measurements of central tendency, the range can reveal the distribution’s spread. When the data collection contains outliers, though, the range can be deceiving. A single outlier in the data will result in a completely different range. The formula for a range is the dataset’s largest value minus the dataset’s smallest value, which gives statisticians a clearer idea of how diverse the data set is.