Median

The median is a statistical measure used to find the central value of a dataset. It is the middle value in a sorted list of numbers or the average of the two middle values if the dataset has an even number of values. The median is a type of average that is not influenced by extreme values, making it a useful measure of central tendency.

Calculation of Median

To find the median of a dataset, follow these steps:

1. Arrange the numbers in the dataset in ascending order from least to greatest.
2. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.

Example:

Consider the dataset: 2, 5, 7, 9, 12

1. Arrange the numbers in ascending order: 2, 5, 7, 9, 12
2. Since the dataset has an odd number of values, the median is the middle value, which is 7.

Properties of Median

1. The median divides the dataset into two equal halves.
2. The median is not affected by extreme values or outliers in the dataset.
3. The median can be used for both numerical and ordinal data.

Use of Median

The median is commonly used in statistics for various purposes:

1. To determine the central tendency of a dataset when outliers are present.
2. To compare datasets with different distributions.
3. To find the middle value in ranked data, such as test scores or ratings.

Conclusion

The median is a statistical measure that provides a robust measure of central tendency. It is calculated by finding the middle value in a sorted list of numbers or the average of the two middle values. The median is not influenced by extreme values and is useful for comparing datasets and finding the middle value in ranked data.