Question

The measure of dispersion which uses only two observations is called_____________

• A. Range
• B. Quartile deviation
• C. Mean deviation
• D. Standard deviation

Hint:

Range calculation:
\[ \text{Range} = \text{Maximum value} - \text{Minimum value} \] - Advantage: Extremely easy and quick to calculate.
- Disadvantage: Uses only two extreme values, ignoring the rest of the dataset.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Measures of dispersion describe the spread or variability of observations in a dataset.
Common measures of dispersion include range, quartile deviation, mean deviation, and standard deviation.
Key Formula or Approach:
The Range (\(R\)) is calculated as:
\[ R = X_{\text{max}} - X_{\text{min}} \] Where \(X_{\text{max}}\) is the maximum value and \(X_{\text{min}}\) is the minimum value in the dataset.

Step 2: Detailed Explanation:
Let us analyze the observations used by each measure of dispersion:
- Range (A):
It is the simplest measure of dispersion.
As shown in its formula, it is calculated using only the two extreme values of the dataset (the maximum and minimum values).
It completely ignores all intermediate values, making it highly sensitive to outliers but very simple to compute.
- Quartile Deviation (B):
It uses two quartile values (\(Q_3\) and \(Q_1\)), which are derived by analyzing the entire dataset to locate the 25th and 75th percentiles.
- Mean Deviation (C) and Standard Deviation (D):
These measures incorporate every single observation in the dataset.
They calculate deviations of each individual value from the mean, making them much more robust and representative of the entire data spread.
Therefore, only the Range uses exactly two observations for its computation.

Step 3: Final Answer:
The measure of dispersion which uses only two observations is called the Range.