Study Calculating Median

Study Median:

Median is the middle value of the element in their ascending order. If the size of the elements is even, then the average value of two middle numbers is the median. In the sequence of elements, divide equally the sequence of elements are on one side, half on the other, then the average value of middle elements is the median.

Study Calculating Median Formulas:

If ‘n’ is the total number of elements and ‘n’ is the ‘odd’, then the formula for finding the middle position after the arrangement of elements in ascending order is: (n+1)/2.

If ‘n’ is the total number of elements and ‘n’ is the ‘even’, then you have to find the two middle positions after the arrangement of elements in ascending order. Formulas for finding the two middle positions are: (n/2) and (n/2)+1. After finding the two middle elements, find the average that is the median.

Study Calculating median - Example Problems:

Study Calculating median Problem 1:

Calculate the median of 5, 4, 1, 8, and 7.

Solution:

Count the elements in the sequence has given.

n = 5(odd)

Arrange the elements in ascending order.

1, 4, 5, 7, 8

Formula for finding the middle position is (n+1)/2

(5+1)/2 = 6/2 = 3

Median = 3.
Study Calculating Median Problem 2:

Calculate the median of 8, 6, 1, 2, 3, 4, 7, and 5

Solution:

Count the elements in the sequence has given.

n = 8(even)

Arrange the numbers in ascending order.

1, 2, 3, 4, 5, 6, 7, 8

Find the two middle positions using n/2 and (n/2)+1

Positions are n/2= 8/2 = 4 and 5

4th and 5th position numbers are 4 and 5

The average is (4+5)/2 = 4.5

Median = 4.5

Study Calculating Median Problem 3:

Calculate the median of 2, 4, 6, 3, 1, 6, 3, 7, 4, and 6

Solution:

Count the elements in the sequence has given.

n = 10(even)

Arrange the numbers in ascending order.

1, 2, 3, 3, 4, 4, 6, 6, 6, 7

Calculate the two middle positions using n/2 and (n/2)+1

Positions are n/2= 10/2 = 5 and 6

4th and 5th position numbers are 4 and 4

The average is (4+4)/2 = 4

Median = 4

Study median practice Problems:

Study median practice problem 1:

Calculate the median of 4, 3, 1, 2, and 6.

Answer: 3
Study median practice Problem 2:

Calculate the median of 7, 9, 1, 4, 3, 6, 2, and 8

Answer: 5
Study median practice Problem 3:

Calculate the median of 5, 4, 6, 2, 3, 1, and 9

Answer: 5