What is median?
Median in math has two meanings. One is the geometric meaning and another is the statistical median.
Geometric median definition:
In a closed plane figure such as a triangle, the line segment that connects the midpoint of one side to the opposite vertex is called the median. See picture below:
The above picture shows a triangle ABC. D, E and F present on the sides AB, BC and CA, so that, AD = DB, CE = EB and AF = FC. The line segments AE, CD and BF are from the triangle ABC. The points where all the three geometric mid-segments intersect is called the centroid of the triangle also called the centre of gravity. In the above figure, O is the centroid of the triangle.
Statistical median definition:
In statistics it is a measure of central tendency. In a frequency distribution, the central value around which most of the values of the variable are centered is called the measure of central tendency. Of the various measures of central tendencies, the most popular are mean, middle number and mode. It is defined as middle value of the data set. For finding median we need to follow the following steps:
1. Arrange the data set in ascending or descending order.
2. If the number of entries is odd, then the middle value would be the (n+1/2)th value.
3. If the number of entries is even, then the middle value would be the average of the (n/2) th and the (n/2 + 1)th value.
4. The value found in step 2 or 3 is called the middle number value.
Sample problem:
1. Find the middle number of the following data set of marks obtained by 10 students in a class test of maximum 10 marks: 8, 8, 9, 5, 5, 6, 6, 7, 6, 4
Solution:
Step 1: Arrange the data in ascending order: 4, 5, 5, 6, 6, 6, 7, 8, 8, 9
Step 2: The number of entries is 10 which is an even number, so we move to step 3.
Step 3: The two middle values would be 10/2 = 5th and 10/2 + 1 = 5+1 = 6th value. Both these are 6. Therefore the middle number is 6.
Median in math has two meanings. One is the geometric meaning and another is the statistical median.
Geometric median definition:
In a closed plane figure such as a triangle, the line segment that connects the midpoint of one side to the opposite vertex is called the median. See picture below:
The above picture shows a triangle ABC. D, E and F present on the sides AB, BC and CA, so that, AD = DB, CE = EB and AF = FC. The line segments AE, CD and BF are from the triangle ABC. The points where all the three geometric mid-segments intersect is called the centroid of the triangle also called the centre of gravity. In the above figure, O is the centroid of the triangle.
Statistical median definition:
In statistics it is a measure of central tendency. In a frequency distribution, the central value around which most of the values of the variable are centered is called the measure of central tendency. Of the various measures of central tendencies, the most popular are mean, middle number and mode. It is defined as middle value of the data set. For finding median we need to follow the following steps:
1. Arrange the data set in ascending or descending order.
2. If the number of entries is odd, then the middle value would be the (n+1/2)th value.
3. If the number of entries is even, then the middle value would be the average of the (n/2) th and the (n/2 + 1)th value.
4. The value found in step 2 or 3 is called the middle number value.
Sample problem:
1. Find the middle number of the following data set of marks obtained by 10 students in a class test of maximum 10 marks: 8, 8, 9, 5, 5, 6, 6, 7, 6, 4
Solution:
Step 1: Arrange the data in ascending order: 4, 5, 5, 6, 6, 6, 7, 8, 8, 9
Step 2: The number of entries is 10 which is an even number, so we move to step 3.
Step 3: The two middle values would be 10/2 = 5th and 10/2 + 1 = 5+1 = 6th value. Both these are 6. Therefore the middle number is 6.
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