Median of Grouped Data


 
 
Concept Explanation
 

Median of Grouped  Data

 Median of ungrouped data, we first arrange the data values of the observations in ascending order. Then , if n is odd, the median is the large (frac{n+1}{2})th observations. And, if n is even, then the median will be average of the large frac{n}{2}th  and the large (frac{n}{2}+1)th  observations.

 

Example:  A survey regarding the height ( in cm ) of 51 girls of Class X of a school was conducted and the following data was obtained:

Height ( in cm ) Number of girls
Less than 140 4
Less than 145 11
Less than 150 29
Less than 155 40
Less than 160 46
Lesss than 165 51

Find the median height.

Solution: To calculate the median height, we need to find the class intervals and their corresponding frequencies.

The given distribution being of the less than type, 140, 145, 150,..., 165 give the upper limits of the corresponding class intervals. So, the classes should be below 140, 140-145, 145-150,....,160-165. Observe that from the given distribution , we find that there are 4 girls with height less than 140, i.e., the frequency of class interval below 140 is 4. Now , there are 11 girls with heights less than 145 and 4 girls with height less than 140. Therefore, the number of girls with height in the interval 140-145 is 11-4=7. Similarly, the frequency of 145-150 is 29-11=18, for 150-155, it is 40-29=11, and so on. So. our frequency distribution table with the given cumulative frequencies becomes:

Class intervals Frequency Cumulative frequency
Below 140 4 4
140-145 7 11
145-150 18 29
150-155 11 40
155-160 6 46
160-165 5 51

Now   large n=51. So,frac{n}{2}=frac{51}{2}=25.5. This observation lies in the class 145-150. Then,

        l ( the lower limit ) = 145

       cf ( the cumulative frequency of the class preceding 145-150) = 11.

        f ( the frequency of the median class 145-150 ) = 18.

       h ( the class size ) = 5.

Using the formula, Median large =l+(frac{frac{n}{2}-cf}{f})times h,   we have

                           Median large =145+(frac{25.5-11}{18})times 5

                                      large =145+frac{72.5}{18}=149.03

.... (More Text Available, Login?)
Sample Questions
(More Questions for each concept available in Login)
Question : 1

Median is that measure of central tendency which divides the total frequency into _________________ equal parts.

Right Option : C
View Explanation
Explanation
Chapters
Content / Category
Class / Course
 
 


Students / Parents Reviews [10]