Median is the measure of central tendency. A data that is properly organized in either ascending or descending order has the middle value as its median. The Median finds its application in the data that is not uniformly distributed but is skewed on either side.

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**Calculation ****of Median**

Let, in a given data, the total number of observations be n.

If n is odd, then the median is the value of { \frac { n+1 }{ 2 } }^{ th } observation.

If n is even, then the median is the average or arithmetic mean of the values of the { \frac { n}{ 2 } }^{ th } and { \frac { n+1 }{ 2 } }^{ th } observations.

**Examples of Median **

**1. ****Choosing the appropriate movie genre**

Suppose, you and your family members go to watch a movie. When you reach the cinema premises, you see that there are three different types of movies available. Now, you are supposed to select the perfect movie that is enjoyable for all the members. Let, the three types of movies available be: animated (best suited for the kids), thriller (liked by the teenage group), and biopic (preferred by the adults). The ages (in years) of people who have visited are- 6, 13, 15, 17, and 60. If you calculate the mean or the average for the following data, it comes out to be 22, which belongs to the adult age group. So, you opt for the biopic. But, in the theatre, you will find only one person to be enjoying it, while the others will get bored. The better alternative in such a case is to calculate the median instead of calculating the mean. The median is the middle value of the properly arranged data, i.e., 15 in this case. When you decide to watch a thriller movie, more people enjoy the cinema day out. The next time, you can apply the concept of median to decide which movie you should watch.

**2. Grouping Data**

Suppose, you have to organize an activity in your class, for which you are supposed to divide the students of the class into two groups. But, you can’t decide how to proceed as you can not abruptly put people into different categories. To do so, you should first decide the factor according to which you want the grouping to be done. For example, let the factor chosen is the height of the students. Now, just note down the height of all the students, and arrange the data in ascending order. Let, the data be arranged as- 152 cm, 158 cm, 160 cm, 162 cm, 189 cm, and 195 cm. If you calculate the median of the above-mentioned data, it comes out to be 161 cm. Now, two groups can be formed very easily, one would be a group of students with a height above 161 cm, while the second group has a height below 161 cm.

**3. Explicating the Poverty Line**

One of the prime applications of the concept of the median lies in the calculation of the poverty line. Let us suppose, we have the information about the monthly income (in INR) of different groups of people in the following range, i.e., 1000, 2000, 3000, 30000, and 80000. The mean comes out to be INR 23,500. If someone employs the concept of mean to set the poverty line, it would be highly inappropriate. This is why we jump to another notion, i.e., median. The median of the above data comes out to be INR 3000, which can more accurately decide that the people below this benchmark are poverty-ridden.

**4. Buying a property**

Buying a property is a peculiar decision in one’s life. Assume that you visit a broker who deals in real estate, he shows you pictures of various houses with their respective prices (in the Indian rupees), 30L, 32L, 38L, 40L, 87L, 90L, and 95L. You ask him for the average price to which he replies INR 60L. Also, you observe that the median price is INR 40L. In this case, you may easily get trapped in the dilemma that the houses with lesser prices might have some flaws in them, while the expensive ones go out of the budget that you have planned. When you consider all the factors, you tend to go with the house worth middle or median price, i.e., INR 40L, and that proves to be the wise decision. Hence, you may consider taking the help of the median while choosing an appropriate property to invest in.

**5. Home budget**

We all tend to plan a monthly budget irrespective of whether we follow it or not. Suppose, every month you spend INR 700 on personal care, INR 100 to pay the water bill, INR 800 on snacks, INR 500 to pay the electricity bill, and INR 6000 to pay the house rent. If you calculate the average expenditure, it comes out to be INR 1,620 by the notion of mean, and INR 700 by employing the median concept. However, the median concept, here, is more efficient because the nature of the data is skewed and asymmetrical.

**6. Business**

Statistics play a key role in business management. Let us say, a businessman who deals in shoes has set distinct prices for different products, say, INR 120, INR 180, INR 250, INR 400, and INR 1000. He needs to improve his business by revising the product cost that is more acceptable to most people. He calculates mean that comes out to be INR 390, while the median comes out to be INR 250. Here, mean will not be that helpful because the person who tends to buy shoes worth INR 400 will find no difference in the new price, i.e., INR 390, while the other person who was able to afford shoes worth INR 120 has to wait until he reaches the average price, i.e., INR 390. On the other hand, the median allows the customers of all sorts to reach a moderate price that they can easily afford. Hence, his business blooms.

**7. ****Median Salary**

Different workplaces have separate rules and regulations. Some of them take the basis of the average salary, while some of them choose the median salary to set a reference. Median salary helps the employees know the middle point of their salaries in their careers. It is also called the 50 per cent income, which means half of the employees work above this median salary, while half of them work below it. This gives a sense of healthy competition and allows them to grow.

Nice breakdown

Thank you so much

This is very informative and well put.