The median of set of nine distinct observations is \(20.5 .\) If each of the observations of the set is increased by 2 , then the median of the new set (1) is increased by 2 (2) is decreased by 2 (3) is two times the original median (4) remains the same as that of the original set

The concept of median is central to understanding how to calculate and adjust data sets. The median is a measure of central tendency that represents the middle value in a sorted list of numbers. It is particularly useful because it is not affected by extremely high or low values (outliers). To find the median of a set of nine distinct observations, you first arrange all the numbers in ascending order. The median is then the fifth number in this ordered list. Unlike the mean, which can be skewed by outliers, the median provides a more accurate representation of the center of a data set.

For example, in the sequence 1, 3, 5, 7, 9, 11, 13, 15, 17, the median is 9 because it is the fifth value. The context of the median within any data set helps in various statistical analyses, ensuring that the middle point is accurately identified without being influenced by disproportionate extremes.

A set of observations is simply a collection or group of numbers or values that we are interested in analyzing. In our exercise, we consider nine distinct observations. This means each number in the set is different from the others. These observations are usually first arranged in a specific order, often ascending.

It's important to understand how to work with these sets of numbers, as the method of arranging and analyzing them directly affects our calculations. In the given exercise, because our set consists of nine distinct values, we know that the median is the fifth observation after sorting. This clear identification helps simplify many statistical computations and ensures accuracy in our results.

When each observation in a set is increased by a certain value, all elements in the set shift up by that amount. This action also affects the median. In our case, all the initial observations are increased by 2. This means every number in our set will be 2 units higher than before.

Practically, if we increase each number in the set by 2, then our original median of 20.5 is now increased to 22.5. This process directly demonstrates that the median increases by the same amount that each observation increases. Therefore, understanding how an increase in value affects the set helps clarify changes in central tendencies like the median and confirms the uniformity of shifts within the set.