Median of Grouped Data
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 th observations. And, if n is even, then the median will be average of the
and the
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 . 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 we have
Median
Median is that measure of central tendency which divides the total frequency into _________________ equal parts. | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [10]
A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
10thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
