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What is The Median?

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In the simplest terms, the median can be defined as the middle value of a given list of data. This value is selected when the list of data is arranged in proper order. One can decide to arrange the numbers in ascending order or descending order. For example, If a student is provided with a list of data in the order of 2, 3, and 4. From this list, the student is asked to find out the median number. The data list is already arranged in proper order, so it is easy to state that 3 is the median.

Apart from this, in Mathematics, the median can also be defined as a type of process that can be used to find the centre value of any set of data. Because of this reason, many people define the median as a measure of central tendency whenever they are asked to explain the answer to the question of what is the median number.

Readers should also be familiar with the fact that apart from the median, there are two other mathematical central tendencies. These measures of central tendencies are mean and mode.

Mean can be defined as the ratio of the sum of all observations or values and the total number of observations. Mode, on the other hand, is the value that is repeated the most in a given data set.

When it comes to geometry, a median is defined as the centre point of a polygon. Students follow several steps when they are trying to learn how to find out the median of a polygon. Also, the median of a triangle is the line segment that joins the vertex of the triangle to the centre of the opposite sides. We can also say that a median bisects the sides of a triangle.

In statistics, the median is a value that lies halfway between the given data set. A median is also the number that is separated by the higher half of a data sample from the lower half of the sample. This means that the value of the median will be different for different types of distributions.

Let’s consider an example to make this topic clearer. Let’s assume that a student has to find the value of the median from a given data set. The data set is 3, 3, 5, 9, 11. In this data distribution, the value of the median is 5. A similar method would work for as long as the total number of observations come up to be an odd number.

But what should one do if the total number of observations in a data set are even? In that case, the student should add both the digits that fall in the middle and, then divide the answer with two. For example, if one has to find the median of a data set: 2, 4, 5, 8, 9, 10, 12, 14, 16, 19, 20, 22. In this data set, both 10 and 12 fall in the middle.

So, we need to 10 + 12 = 22

22 / 2 = 11

This means that 11 is the medial of even numbers provided in the data set that was mentioned above.


The Median Formula

Till now, we have looked at the basic process of finding out the value of median in a simple data set. The next step is to understand the median formula even. Readers must remember that the formula for calculating median for even and an odd number of observations is different. This is why it is important to first identify the total number of observations in a data set before applying the even median formula.


Case 1: Odd Number of Observations

If the total number of observations in a data set is odd, then the following formula for calculating median can be applied.

Median = {(n + 1) / 2}th term

In this median sums formula, n is the total number of observations. This formula works for calculating the median of odd numbers.


Case 2: Even Number of Observations

If the total number of observations in a data set comes up to be an even number, then the median even formula should be followed. The median of even numbers formula is mentioned below.

Median = [(n / 2)th term + {(n / 2) + 1th] / 2

In this median formula for even numbers, n is the total number of observations.


How Can You Calculate the Value of Median of Data?

Calculating the value of the median of a complex set of data is not easy. However, one can follow a simple process to arrive at the final answer. First, one needs to begin by arranging the observations in an ascending or descending order. This is done as the middle value of the set of observations will provide the median of numbers.

However, there are still two scenarios that can arise in this case before arriving at the final answer. The total number of observations can either be odd or even. A different formula is used in both cases.

If one wants to find the value of the median of a set of numbers that are odd, then the formula mentioned below can be used.

Median = (n + 1 / 2)th observation

If one wants to know how to find the median number of a set of data that has an even number of observations, then the formula that is mentioned below is used.

Median = Mean of (n / 2)th and [(n / 2) + 1]th observations


The Graphical Representation of Median

Till now, we have answered questions like what is a median and what formulas are required for the median. It is now time to gain better insight into this topic by going over the graphical representation of the median.

There are three main central tendencies. These three central tendencies are mean, median, and mode. All three values are different and can be plotted differently on a graph. If you wish to learn how these values are plotted, then you should look at the image that is attached below. Students also often have to solve questions in which they have to graphically represent the values of median, mean, or mode. This image will help students answer those types of questions.

[Image will be Uploaded Soon]


Fun Facts about Median and Other Measures of Central Tendency

Did you know that mean is the most commonly used measure of central tendency? Mean can be defined as the average of all the observations in the data set. This measure of central tendency is applicable in the case of both continuous and discrete data.

Mean can also be defined as the sum of all the values of observations in data divided by the total number of observations. On the other hand, the mode is the most frequently occurring value in the data set. All these three values of central tendencies help in providing better insight into a data set and are of great importance in the subject of statistics.

FAQ (Frequently Asked Questions)

1. Define What you Mean by the Median with an Example.

Answer: Median can be defined as the central value in a given set of data when it is arranged in proper order. For example, if one has collected a list of observations that contains the following values. 33, 55, 77, 22, 11. After arranging the values, the data set can be viewed as 11, 22, 33, 55, 77. Hence, it can be said that the value of the median is 33.

2. How Can One Calculate the Median of a Data Set that Contains 10 Observations?

Answer: 10 is an even number. This is why the median formula for even number of observations will be used in this case.

3. What is the Difference Between the Median and Mean?

Answer: Median is the centre value of the ordered list of observations. Mean, on the other hand, is the ratio of the sum of the list of values and the number of values. When it comes to calculating mean, the order of values does not matter.

4. Find the Median of 14, 63, and 55.

Answer: We get 14, 55, 63 by arranging the value of ascending order. The middle number is 55. This means that the median is 55.

5. Sharon’s Family Drove through Seven States on Summer Vacation. The Price of Gasoline Differed in Different States. Those Prices are 1.79, 1.61, 2.09, 1.84, 1.96, 2.11, 1.75. Use this Data to Calculate the Median of Gasoline Cost.

Answer: If we arrange the data from smallest to greatest, then we get:

1.61, 1.75, 1.79, 1.84, 1.96, 2.09, 2.11

Since the total number of observations is odd, then we only have to identify the middle value from this list. This middle value is 1.84. This means that the median of this data set is 1.84.