Question

describe how the range of a distribution is defined and calculated.
choose the correct answer below.
a. the range of a data set is the difference between its median and most extreme value.
b. the range of a data set divides the lowest fourth of a data set from the upper three - fourths
c. the range of a data set is the difference between its highest and lowest data values
d. the range of a data set divides the lowest three - fourths of a data set from the upper fourth.

Explanation:

The range is a measure of dispersion. It is calculated by subtracting the smallest value from the largest value in a data set.

• Option A: Incorrect. The range is not related to the median.
• Option B: Incorrect. This description is about quartiles (specifically the first quartile \(Q_1\)), not the range.
• Option C: Correct. The formula for the range \(R\) is \(R=\text{Max}-\text{Min}\), where \(\text{Max}\) is the highest data value and \(\text{Min}\) is the lowest data value.
• Option D: Incorrect. This description is about quartiles (specifically the third quartile \(Q_3\)), not the range.

Answer:

C. The range of a data set is the difference between its highest and lowest data values.