How To Calculate Median in Mathematics: Definition, Formula, and Examples
Definition: Median is a statistical measure that represents the middle value of a set of numerical data.
Formula: To calculate the median of a data set, the values must first be arranged in numerical order. If the number of values in the data set is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.
Types of Median in Mathematics:
- Sample Median: This is the median calculated from a sample of a larger population.
- Population Median: This is the median calculated from an entire population.
Need for Median:
- Describing Data: Median is used to describe the central tendency of a data set, providing valuable information about the typical value in the data.
- Comparison: Median can be used to compare data sets and determine if they are similar or different.
- Outlier Detection: Median is not sensitive to outliers like the mean, so it can be used to identify and exclude extreme values from a data set.
How to Use Median:
- Arrange the values in the data set in numerical order.
- If the number of values in the data set is odd, the median is the middle value.
- If the number of values in the data set is even, the median is the average of the two middle values.
Example: Consider the data set [1, 2, 3, 4, 5]. To find the median, the values are first arranged in numerical order, [1, 2, 3, 4, 5]. Since the number of values is odd, the median is the middle value, which is 3.
Note: The median is a robust statistic that is less affected by outliers and extreme values compared to the mean. It is often used to summarize the central tendency of data that is not normally distributed.