Subscribe to our YouTube channel for the latest videos, updates, and tips.


Finding the Median of Grouped Data

To find the median of arrayed (grouped) data we need to follow the following steps:

Step I: Arrange the grouped data in ascending or descending order, and form a frequency table.

Step II: Prepare a cumulative-frequency table of the data.

Step III: Select the cumulative frequency that is just greater than N2, where N is the total number of observations (variates). Then find the median as follows.

The variate whose cumulative frequency is the selected cumulative frequency, is the median of the data.

If N2 is equal to the cumulative frequency of a variate then

median = mean of this variate and the variate just greater than it.

Solved Examples on Find the Median of Grouped Data /Arrayed Data:

1. Find the median of the following distribution.


Variate

2

5

6

8

10

Number of Students

3

2

5

4

2


Solution:

Here, the frequency distribution is given.

The cumulative-frequency table of the distribution is

Variates

2

5

6

8

10

Frequency

3

2

5

4

                  2       

N = 16

Cumulative Frequency

3

5

10

14

16

Finding the Median of Grouped Data

Here, N2 = 162 = 8.

The cumulative frequency just greater than 8 is 10.

The variate whose cumulative frequency is 10 is 6.

Therefore, the median = 6.


2. Find the median of the arrayed data given below.

10, 11, 11, 12, 12, 12, 13, 14, 14, 15, 15, 15, 15, 16, 16, 17, 18, 19, 19, 20.

Solution:

Putting the data in a frequency table, we have the cumulative frequencies as below.

Problems on Median of Grouped Data

Here, the total frequency N = 20.

So, N2 = 202 = 10.

The cumulative frequency just greater than 10 is 13 and the corresponding variates is 15. So, the median = 15.






9th Grade Math

From Finding the Median of Grouped 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. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  2. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  3. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More