Range
The range of a set of data is the difference between the largest and smallest values in the set. It is a simple measure of dispersion, and it is calculated as follows:
Range = Largest value - smallest value
For example, if the data set is {1, 3, 5, 7, 9}, then the range is 9 – 1 = 8.
The range is a useful measure of dispersion because it is easy to calculate and it can be interpreted easily. However, it is not a very sensitive measure of dispersion, meaning that it can be misleading if the data set is not normally distributed.
Coefficient of Range
The coefficient of range is a relative measure of dispersion that is calculated as the ratio of the range to the mean of the data set. It is expressed as a percentage, and it is calculated as follows:
Coefficient of Range = (Range / Mean) * 100
For example, if the data set is {1, 3, 5, 7, 9} and the mean is 5, then the coefficient of range is (8 / 5) * 100 = 64%.
The coefficient of range is a more sensitive measure of dispersion than the range, but it is also more difficult to calculate. It is also more affected by outliers, meaning that it can be misleading if the data set contains outliers.
Mathematical Formulas
The following are the mathematical formulas for the range and coefficient of range:
- Range = Largest value – smallest value
- Coefficient of Range = (Range / Mean) * 100
MCQs on Range and Coefficient of Range
Here are some MCQs on range and coefficient of range:
- What is the range of the data set {1, 3, 5, 7, 9}?
- A. 1
- B. 3
- C. 5
- D. 7
- E. 9
The correct answer is (C). The range is the difference between the largest and smallest values in the set, so the range is 9 – 1 = 8.
- What is the coefficient of range of the data set {1, 3, 5, 7, 9} if the mean is 5?
- A. 16%
- B. 32%
- C. 48%
- D. 64%
- E. 80%
The correct answer is (D). The coefficient of range is the ratio of the range to the mean, so the coefficient of range is (8 / 5) * 100 = 64%.
- The coefficient of range of a data set is 50%. What is the ratio of the range to the mean?
- A. 1
- B. 2
- C. 3
- D. 4
- E. 5
The correct answer is (A). The coefficient of range is the ratio of the range to the mean, so if the coefficient of range is 50%, then the ratio of the range to the mean is 1.
- The range of a data set is 10. What is the coefficient of range if the mean is 20?
- A. 5%
- B. 10%
- C. 20%
- D. 30%
- E. 40%
The correct answer is (C). The coefficient of range is the ratio of the range to the mean, so the coefficient of range is (10 / 20) * 100 = 50%.
- The coefficient of range of a data set is 25%. If the mean of the data set is increased by 50%, what will be the new coefficient of range?
The new coefficient of range will be 12.5%. This is because the coefficient of range is a relative measure of dispersion, and it is not affected by changes in the mean.
Conclusion
The range and coefficient of range are two measures of dispersion. The range is a simple measure that is easy to calculate, but it is not very sensitive to changes in the data set. The coefficient of range is a more sensitive measure of dispersion, but it is also more difficult to calculate.