The median is a measure of
a. relative dispersion
b. absolute dispersion
c. central location
d. relative location
The correct answer and explanation is :
The correct answer is c. central location.
Explanation:
The median is a measure of central location (or central tendency), which is used to describe the middle point of a data set. It represents the value that divides a data set into two equal halves. In other words, 50% of the data points are smaller than the median, and 50% are larger.
Here’s how the median works:
- To find the median, the data set is first ordered in ascending or descending order.
- If the data set has an odd number of values, the median is simply the middle number.
- If the data set has an even number of values, the median is the average of the two middle values.
The median is often preferred over the mean (another measure of central tendency) in certain situations, especially when a data set has outliers or is skewed. This is because the median is not affected by extremely large or small values, making it a better measure of central location for skewed distributions.
Example:
Consider the data set: [2, 3, 5, 8, 10]
- Since there are five values (an odd number), the median is the middle value, which is 5.
For an even number of values, such as: [2, 3, 5, 8]
- The median is the average of the two middle values: $\frac{3 + 5}{2} = 4$.
Why Not the Other Options?
- a. Relative Dispersion refers to measures that describe the spread of data relative to the central value, such as the coefficient of variation. The median does not measure spread.
- b. Absolute Dispersion is related to the spread of data, measured by range, variance, or standard deviation. The median does not give any information about spread or variability.
- d. Relative Location is not a typical term used in statistics, so this option doesn’t apply to the median.
In summary, the median is a useful tool for identifying the central value in a data set, particularly in situations where data may be skewed or contain outliers.