What is a median in math?
The median in mathematics is used to find the middle value of a given data. The value which is derived in the middle after arranging the data in ascending or descending order is called the median of the data. When explaining a set of data, the central position of the data set is taken out, and it is used in the median formula. This is defined as the central measure of tendency.
Median is the middle value of any group. It is that point where half the data is more and half the data is less. Median represents many data points with a single data point. The median is the easiest statistical method to calculate. For finding out the median, the data has to be sorted in ascending order, and then the middlemost data point indicates the median of the data.
When the data is odd, then the median is the middlemost data. When the data is even, the median is the average of the two middle values.
Median Definition
The value of the middle-most observation which is found out after arranging the data in ascending order is defined as the median of the data. Many times, it is not that easy to consider the complete data for representation. Then in such cases, median becomes useful. The median is an easy statistical metric to calculate. Median is also known as the Place Average because the data which is placed in the middle of a sequence is taken as the median.
What is the median formula?
The median formula differs depending on the number of observations and whether they are odd or even. With the help of the median formula, the middle value of the arranged set of numbers can be found out. In order to find out the measure of central tendency, the components of the group in increasing order are to noted down.
Let us now find out the median of data by taking an example.
· Step 1: Let us take the data: 4,4,6,3, and 2. Let us now arrange this data in ascending order: 2, 3, 4, 4, 6.
· Step 2: Now the number of values is calculated which is 5.
· Step 3: Let us find out the middle value or the median which is 4.
How to find the median of two numbers?
In an arranged order, the median is the number which is in the middle between the range extremes. It is not similar with the mean. Let us find out the median. If two set of values are given, then the median will be identical to the mean, or arithmetic average. For example, the mean and median of the numbers 2 and 10 is 6. it is to be noted down that the median is the value which is at the middle-point of the dataset, and it is not the middle-point of the values. The mean is the arithmetic average: (10= 2)/2 = 6. Now if two more numbers are added, say 3 and 4. Then the median will be 3.5 and the mean will be (2 + 3 + 4 + 10)/4 = 4.75.
Median Formula When n is Odd
The median formula of a given set of numbers, having “n” odd observations, can be expressed as:
Median for Odd Data
Median Formula When n is Even
The median formula of a given set of numbers, having “n” even observations, can be expressed as:
Median for Even Data
How to use median formula?
The median formula is used to find the median value of given data. Following are the steps to calculate the median value by using median formula:
· Step 1: The given data is to be sorted out in increasing order
· Step 2: The number of observations has to be counted
· Step 3: If the number of observations is odd, then this median formula is used:
· Step 4: if the number of observations is even, then this median formula is used:
Now let us use the above steps in the below given practical illustration in order to understand the median formula.
Illustration: Let us suppose that there are 5 top management employees in an organization. The salaries which are given to the employees are $5,000, $6,000, $4,000, $8,000 and $7,500. Calculate the median salary by using the median formula.
Solution: Now we will follow the above-mentioned steps to find the median salary.
· Step 1: Let us sort the data in increasing order, $4,000, $5,000, $6,000, $7,500, and $8,000.
· Step 2: The total number of observations = 5
· Step 3: The given number of observations is odd.
· Step 4: Now by using the median formula for odd observation,
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