The simplest possible measure of dispersion, which is defined as the difference between the values of the extreme items of a series, is called:

Correct option is C

Range

Range is the simplest measure of dispersion in statistics. It is calculated as the difference between the maximum and minimum values in a given dataset.

Mathematically, it is expressed as:

$$\text{Range}=\text{Maximum Value}-\text{Minimum Value}$$

Why is it a measure of dispersion?

• • Dispersion measures how spread out the data is.
  • The range provides a quick and easy way to understand the spread of data but does not take into account the distribution of all data points.

Thus, the correct answer is "Range" (Option 3).

Information Booster:

• Range is useful for understanding variability but does not account for individual variations in the dataset.

• It is highly sensitive to outliers, meaning extreme values can greatly affect the range.

• Other measures of dispersion, such as standard deviation and interquartile range, provide more detailed insights into data spread.

• Example: If a dataset contains values (5, 10, 15, 20, 25), the range is:

  $$25-5=20$$

• Applications of Range:

  • Used in weather forecasting to measure temperature fluctuations.
  • Applied in finance to assess stock price volatility.
  • Useful in quality control to analyze product variations.

Additional Information:

• Mean (Option 1): The average of all values in a dataset, calculated as:

  Mean=∑Xn\text{Mean} = \frac{\sum X}{n}Mean=n∑X​

• Median (Option 2): The middle value of an ordered dataset, dividing it into two equal halves.

• Mode (Option 4): The most frequently occurring value in a dataset.