What is the midrange and how is it obtained?
Choose the correct answer below.
A. The midrange is a value that is representative of a data set. It is found by subtracting the lowest and highest data values and dividing the difference by 2 .
B. The midrange is a value that is representative of a data set. It is found by adding the lowest and highest data values and dividing the sum by 2
C. The midrange is the average value of the data set. It is found by adding the lowest and highest data values and dividing the sum by 2
D. The midrange is the average value of the data set. It is found by subtracting the lowest and highest data values and dividing the difference by 2
The Correct Answer and Explanation is :
The correct answer is B: The midrange is a value that is representative of a data set. It is found by adding the lowest and highest data values and dividing the sum by 2.
Explanation:
The midrange is a measure of central tendency that gives a rough idea of the “center” of a data set. It is calculated using the smallest (minimum) and largest (maximum) values in the data set. By taking the sum of these two values and dividing by 2, we can obtain the midrange, which effectively gives the midpoint between the extreme values of the data set.
Mathematically, the midrange is calculated as:
[
\text{Midrange} = \frac{\text{Minimum value} + \text{Maximum value}}{2}
]
Why this works:
- The midrange provides a simple estimate of the central point in a data set, particularly useful for datasets where the range of values is not too large or skewed.
- Since it only considers the two extreme values (the minimum and maximum), the midrange can be sensitive to outliers. If a data set contains unusually high or low values, the midrange may not represent the “typical” value well.
- It is different from the median or mean, which use more of the data points to describe the central tendency. The median, for example, is found by locating the middle value when the data is ordered, and the mean is the sum of all data points divided by the number of points.
Example:
Consider the data set: 2, 5, 8, 10, 12
- The minimum value is 2, and the maximum value is 12.
- The midrange would be calculated as:
[
\text{Midrange} = \frac{2 + 12}{2} = \frac{14}{2} = 7
]
Thus, the midrange of this data set is 7.
In conclusion, the midrange is a straightforward method for approximating the center of a data set, but it may not always provide an accurate reflection of the data, especially when there are outliers. It is mainly used for its simplicity in situations where you only need an approximate value.