Which of the following is NOT a characteristic of the midrange?
A It is robust to outliers.
B It is useful when you have only the maximum and minimum values of a data set.
C It is halfway between the lowest and highest values.
D It is easy to calculate
The correct answer and explanation is:
The correct answer is A: It is robust to outliers.
Explanation:
The midrange is a simple measure of central tendency in a data set. It is calculated by finding the average of the highest and lowest values in the data set, i.e., (max value+min value)/2(\text{max value} + \text{min value}) / 2. Here’s a breakdown of the options:
- Option A: It is robust to outliers
This is incorrect. The midrange is not robust to outliers. Since it only relies on the highest and lowest values in the data set, extreme outliers will heavily influence the midrange. For example, if a data set has a value of 1000 along with other values ranging from 1 to 10, the midrange will be distorted by the 1000, making it less representative of the overall distribution of data. - Option B: It is useful when you have only the maximum and minimum values of a data set
This is correct. The midrange is particularly useful when you have limited information, such as only knowing the maximum and minimum values. It gives a quick estimate of the central point of the data, even without knowing the full distribution. - Option C: It is halfway between the lowest and highest values
This is also correct. By definition, the midrange is calculated as the average of the minimum and maximum values, so it is essentially halfway between them. - Option D: It is easy to calculate
This is true as well. The midrange is one of the easiest measures to compute because it requires only the highest and lowest values from the data set.
In summary, the midrange is a simple and quick measure, but its main weakness is that it can be heavily affected by outliers, unlike other measures of central tendency, such as the median or mean, which are more robust in such cases.