Question

Range of data 5, 10, 15, 20 is ____.

• A. 10
• B. 15
• C. 20
• D. 5

Hint:

While the Range is easy to calculate, it only considers the two extreme values and ignores everything in between. This makes it very sensitive to "outliers" (unusually high or low numbers).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The range is the simplest measure of dispersion in a data set. It represents the total spread between the smallest and the largest values.

Step 2: Key Formula or Approach:
\[ \text{Range} = \text{Maximum Value} - \text{Minimum Value} \]

Step 3: Detailed Explanation:
In the given data set $\{5, 10, 15, 20\}$: 1. The Maximum (largest) value is 20. 2. The Minimum (smallest) value is 5. 3. Calculation: \[ \text{Range} = 20 - 5 = 15 \]

Step 4: Final Answer:
The range of the data is 15.

Answer 2

The question asks for the range of the data set 5, 10, 15, 20. The range measures the spread of the data as the difference between its largest and smallest values. Let's check each option.

1. 10: This is the difference between 15 and 5, or between 20 and 10, but neither pair represents the true maximum and minimum of the whole set, so this is not the range.
2. 15: The largest value in the set is 20 and the smallest is 5. Subtracting, \( 20 - 5 = 15 \), which correctly captures the full spread between the two extreme values of the data.
3. 20: This is simply the maximum value of the set on its own, not a difference between the maximum and minimum, so it cannot represent the range.
4. 5: This is the smallest value in the set, and also the common difference between consecutive terms, but it is not the difference between the overall largest and smallest values.

Only subtracting the true minimum (5) from the true maximum (20) gives the correct spread of the data.

Therefore, the correct answer is 15.