Median of Raw Data

The median of raw data is the number which divides the observations when arranged in an order (ascending or descending) in two equal parts.


Method of finding median         

Take the following steps to find the median of raw data.

Step I: Arrange the raw data in ascending or descending order.

Step II: Observe the number of variates in the data. Let the number of variates in the data be n. Then find the median as following.

(i) If n is odd then \(\frac{n + 1}{2}\)th variate is the median.

(ii) If n is even then the mean of \(\frac{n}{2}\)th and (\(\frac{n}{2}\) + 1)th variates is the median, i.e.,

median = \(\frac{1}{2}\left \{\frac{n}{2}\textrm{th Variate} + \left (\frac{n}{2} + 1\right)\textrm{th Variate}\right \}\).

Solved Examples on Median of Raw Data or Median of Ungrouped Data:

1. Find the median of the ungrouped data.

15, 18, 10, 6, 14

Solution:

Arranging variates in ascending order, we get

6, 10, 14, 15, 18.

The number of variates = 5, which is odd.

Therefore, median = \(\frac{5 + 1}{2}\)th variate  

                            = 3rd variate

                            = 14.


2. Find the median of the raw data.

8, 7, 15, 12, 10, 8, 9

Solution:

Arranging the variates in ascending order, we get

7, 8, 8, 9, 10, 12, 15.

The number of variates = 7, which is odd.

Therefore, median = the \(\frac{7 + 1}{2}\)th variate  

                            = 4th variate

                            = 9.


3. Find the median of the ungrouped data.

10, 17, 16, 21, 13, 18, 12, 10.

Solution:

Arranging the variates in ascending order, we get

10, 17, 16, 21, 13, 18, 12, 10.

The number of variates = 8, which is even.

Therefore, median = mean of the \(\frac{8}{2}\)th and (\(\frac{8}{2}\) + 1)th variate

                            = mean of the 4th and 5th variates

                            = mean of 13 and 16

                            = (\(\frac{13 + 16}{2}\)

                            = (\(\frac{29}{2}\)

                            = 14.5.

Median of Raw Data

4. Find the median of the raw data.

8, 7, 5, 6, 3, 8, 5, 3

Solution:

Arranging variates in descending order, we get

8, 8, 7, 6, 5, 5, 3, 3.

The number of variates = 8, which is even.

Therefore, median = mean of \(\frac{8}{2}\)th and (\(\frac{8}{2}\) + 1)th variate

                            = mean of 4th and 5th variate

                            = mean of 6 and 5

                            = \(\frac{6 + 5}{2}\)

                            = 5.5

Note: The median need not be form among the variates.





9th Grade Math

From Median of Raw Data to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line

    Dec 14, 24 02:12 PM

    Curved Line and Straight Line
    2nd grade geometry worksheet

    Read More

  2. 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

    Dec 14, 24 12:25 PM

    2nd Grade Math Worksheet
    2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

    Read More

  3. Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns

    Dec 13, 24 08:43 AM

    Complete the Series Patterns
    We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r…

    Read More

  4. Patterns in Math | Missing Number | Counting Numbers | Worksheets

    Dec 13, 24 12:31 AM

    Finding patterns in math is very important to understand the sequence in the series. We need to find the exact missing number that from the group of numbers. The counting numbers may be counting

    Read More

  5. Concept of Pattern | Similar Patterns in Mathematics | Similar Pattern

    Dec 12, 24 11:22 PM

    Patterns in Necklace
    Concept of pattern will help us to learn the basic number patterns and table patterns. Animals such as all cows, all lions, all dogs and all other animals have dissimilar features. All mangoes have si…

    Read More