Question

Calculate the range and coefficient of range from the following data :
50, 80, 100, 120, 150, 180, 200

• A. 200, 50%
• B. 150, 60%
• C. 150, 50%
• D. 250, 60%

Hint:

The Coefficient of Range is a relative measure of dispersion. It is unitless and allows for comparing the variability of different datasets, unlike the absolute Range.

Answer 1

The Correct Option is B

Step 1: Concept:
The question asks for two fundamental measures of statistical dispersion: the Range and the Coefficient of Range for a given numerical dataset.

Step 2: Key Formula or Approach:
The formulas for these measures are:
\[ \text{Range} = L - S \]
\[ \text{Coefficient of Range} = \frac{L - S}{L + S} \times 100\% \]
where \( L \) is the largest value and \( S \) is the smallest value in the dataset.

Step 3: Step-by-step Explanation:

• First, identify the extreme values in the given sorted dataset (50, 80, 100, 120, 150, 180, 200).

• Smallest value (\( S \)) = 50.

• Largest value (\( L \)) = 200.

• Calculating Range:
\[ \text{Range} = 200 - 50 = 150 \]

• Calculating Coefficient of Range:
\[ \text{Coefficient of Range} = \frac{200 - 50}{200 + 50} \]
\[ \text{Coefficient of Range} = \frac{150}{250} \]
\[ \text{Coefficient of Range} = 0.60 \]

• To express this as a percentage (as seen in the options), multiply by 100:
\[ 0.60 \times 100\% = 60\% \]

Step 4: Final Answer:
The Range is 150 and the Coefficient of Range is 60%, which corresponds to Option (B).