A median is a positional number that determines the position of the middle set of data. It divides the set of data into two parts. In which, one part includes all the greater values or which is equal to a median value and the other set includes all lesser values or equal to the median. In simple words, the median is the middle value when a data set is organized according to the magnitude. The value of the median remains unchanged if the size of the largest value increases because it is defined by the position of various value.
To evaluate the median the value must be arranged in the sequence of numbers, and the numbers should be arranged in the value order starting from lowest to highest. For instance, while evaluating the medium if there is any sort of odd amount of number in the list, the median will be the middle number, with a similar number presented below or above. However, if the amount is an even number than the middle pair must be evaluated, combined together, and divided by two to find the median value.
Meaning, Merits and Demerits of Median
Q.1 MEDIAN 
It divides the series into two equal parts. One part comprises all values greater than the median and the other part comprises all values smaller than the median. 
Q.2BRIEFLY EXPLAIN THE MERITS AND DEMERITS OF MEDIAN.  
ANSWER: (A) FOLLOWING ARE SOME OF THE MERITS OF MEDIAN: 

(1) EASY TO CALCULATE AND SIMPLE TO UNDERSTAND 

(2) NOT AFFECTED BY EXTREME VALUES 

(3) RIGIDLY DEFINED 

(4) BEST AVERAGE IN CASE OF QUALITATIVE DATA 

(5) USEFUL IN CASE OF OPEN ENDED DISTRIBUTION 

(6) REPRESENTED GRAPHICALLY 

(B) FOLLOWING ARE SOME OF THE DEMERITS OF MEDIAN:  
(1) ARRANGEMENT OF DATA IS NECESSARY 

(2) NOT BASED ON ALL THE OBSERVATIONS 

(3) NOT A REPRESENTIVE OF THE UNIVERSE 

(4) AFFECTED BY FLUCTUATIONS IN SAMPLING 

(5) LACK OF FURTHER ALGEBRAIC TREATMENT 

Q.3LIST THE PROPERTIES OF MEDIAN.  
ANSWER:  
PROPERTIES OF MEDIAN 

Q.4DEFINE PARTITIONAL VALUES. WHAT IS MEANT BY FIRST, SECOND AND THIRD QUARTILE?  
ANSWER:  
(A) PARTITIONAL VALUES  Partition values are the values which are obtained by dividing a series into more than two parts. 
(B) QUARTILES:  
TYPES WITH THEIR MEANING 
It divides the distribution in such a way that the onefourth (25%) of total items fall below it and threefourth (75%) are above it.
It divides the distribution in such a way that threefourth (75%) of total items fall below it and onefourth (25%) are above it. 
Practice Questions:
INDIVIDUAL SERIES
Q.1 FOLLOWING IS THE DATA REGARDING HEIGHT OF SEVEN STUDENTS. YOU ARE REQUIRED TO COMPUTE THEIR MEDIAN HEIGHT:  
Height (in Cm.)  162  122  161  165  160  169  198  
Q.2 IN A HOSPITAL A PATIENT WAS OPERATED UPON AND POST OPERATION DATA WAS COLLECTED REGARDING HIS BODY TEMPERATURE AFTER EVERY HOUR FOR THE FIRST EIGHT HOURS TO TAKE DECISION ABOUT MEDICINES. FIND MEDIAN BODY TEMPERATURE OF THE PATIENT.  
Time  1pm  2pm  3pm  4pm  5pm  6pm  7pm  8pm  
Temperature (°f)  98.5  99  100  100  101  101  101  102 
DISCRETE SERIES
Q.1 CALCULATE MEDIAN SIZE OF SHOES OF STUDENTS OF CLASS XI FROM THE FOLLOWING DATA:  
Size of Shoes  5  6  7  8  9  10  
No. of Students  2  10  15  11  1  1  
Q.2 FIND MEDIAN WEIGHT OF PINEAPPLE FROM THE FOLLOWING DATA:  
Weight of Pineapple (in Gms.)  800  950  1100  1150  1250  1300  1400  1500  1850  2,000  
Quantity (Pcs.)  3  11  8  10  18  7  6  7  3  2  
Q.2 SUBHASH A FRUIT VENDOR BOUGHT A SAC OF PINEAPPLE HAVING 75 PIECES FROM THE WHOLESALE FRUIT MARKET. HE HAS ARRANGED ALL THE PIECES AND KEPT THEM IN THE ASCENDING ORDER OF ESTIMATED WEIGHT. HE WANT TO KNOW THE ESTIMATED AVERAGE WEIGHT HELP HIM TO FIND AVERAGE WEIGHT HE WANT TO KNOW THE AVERAGE FROM THE FOLLOWING, FIND MEDIAN WEIGHT OF PINEAPPLES: 
CONTINUOUS SERIES
(A) MEDIAN FROM EXCLUSIVE CONTINUOUS SERIES  
Q.1 USING MEDIAN, FIND ESTIMATED CASH WITHDRAWN BY ONE CUSTOMER FROM THE FOLLOWING:  
CASH
WITHDRAWN (RS.) 
0–500  500–1,000  1,000–1,500  1,500–2,000  2,000–2,500  2,5003,000  
NO. OF CUSTOMERS  12  20  25  23  7  13  
(B) MEDIAN FROM INCLUSIVE CONTINUOUS SERIES  
Q.2 FROM THE FOLLOWING, FIND MEDIAN SIZE.  
SIZE (Units)  10 – 19  20 – 29  30 – 39  40 – 49  50 – 59  60 – 69  
FREQUENCY  5  9  10  14  8  4  
(C) MEDIAN FROM MID VALUE SERIES  
Q.3 FIND MEDIAN FROM THE FOLLOWING:  
Mid Values  8  16  24  32  40  48  
Frequency  3  8  16  15  10  8  
(D) MEDIAN FROM INVERTED/DESCENDING EXCLUSIVE CONTINUOUS SERIES  
Q.4 USING MEDIAN COMPUTE AVERAGE AGE FROM THE FOLLOWING.  
Age (in Years)  50 – 60  40 – 50  30 – 40  20 – 30  10 – 20  0 – 10  
Number of Persons  9  12  15  7  5  2  
(E) MEDIAN FROM CONTINUOUS SERIES WITH UNEQUAL INTERVALS  
Q.5 FIND MEDIAN FROM THE FOLLOWING.  
Class  0 – 2  2 – 10  10 – 30  30 – 50  50 – 80  80 – 100  
Frequency  20  5  2  3  12  6  
(F) MEDIAN FROM LESS THAN CUMULATIVE FREQUENCY DISTRIBUTION  
Q.6 FIND AVERAGE AGE USING MEDIAN FROM THE FOLLOWING DATA.  
Age (in Years)  Less than 10  Less than 20  Less than 30  Less than 40  Less than 50  Less than 60  
No. of Persons  5  20  45  78  90  100  
(G) MEDIAN FROM MORE THAN SERIES/CUMULATIVE FREQUENCY DISTRIBUTION  
Q.7 FIND MEDIAN MARKS FROM THE FOLLOWING DATA:  
Marks  More than 10  More than 20  More than 30  More than 40  More than 50  More than 60  
No. of Students  100  85  75  45  5  2  
(H) MEDIAN FROM OPEN END SERIES  
Q.8 CALCULATE MEDIAN WEIGHT OF CLASS XII STUDENTS FROM THE FOLLOWING DATA:  
WEIGHT (In Kg)  Below 40  40 – 45  50 – 60  60 – 75  75 – 85  85 and Above  
Number of Students  3  5  14  10  7  1 
MISSING FIGURE
Q.1 FIND THE MISSING FREQUENCY OF CLASS 3040, IF MEDIAN OF THE SERIES IS 28.  
CLASS  0 – 10  10 – 20  20 – 30  30 – 40  40 – 50  50 – 60 
FREQUENCY  12  18  –  20  19  6 
LOCATING MEDIAN GRAPHICALLY
MEDIAN FROM LESS THAN OGIVE
Q.1 FROM THE FOLLOWING DRAW LESS THAN CUMULATIVE FREQUENCY CURVE i.e. “LESS THAN OGIVE” AND LOCATE MEDIAN:  
MARKS  0 – 10  10 – 20  20 – 30  30 – 40  40 – 50  50 – 60 
NUMBER OF STUDENTS  6  15  25  20  10  4 
MEDIAN FROM MORE THAN OGIVE
Q.2 DRAW MORE THAN OGIVE AND LOCATE MEDIAN.  
MARKS  0 – 10  10 – 20  20 – 30  30 – 40  40 – 50  50 – 60 
NUMBER OF STUDENTS  6  15  25  20  10  4 
MEDIAN FROM LESS THAN AND MORE THAN OGIVE
Q.3 DRAW LESS THAN AND MORE THAN OGIVE AND LOCATE MEDIAN. ALSO VERIFY YOUR ANSWER.  
MARKS  0 – 10  10 – 20  20 – 30  30 – 40  40 – 50  50 – 60 
NUMBER OF STUDENTS  6  15  25  20  10  4 
QUARTILE DEVIATION
INDIVIDUAL SERIES
Q.1 FOLLOWINGIS THE DATA OF MARKS OF 11 STUDENTS. YOU ARE REQUIRED TO LOCATE VALUE OF LOWER QUARTILE AND UPPER QUARTILE.  
MARKS  45  39  38  67  90  86  76  40  84  53  70  
Q.2 FOLLOWING IS THE DATA MARKS OF TWELVE STUDENTS. YOU ARE REQUIRED TO LOCATE VALUE OF LOWER QUARTILE AND UPPER QUARTILE:  
MONTHLY INCOME (`)  3,500  5,000  2,800  10,000  50,000  4,500  1,00,000  3,000  8,000 
DISCRETE SERIES
Q.2 CALCULATE LOWER QUARTILE AND UPPER QUARTILE FROM THE FOLLOWING DATA:  
Scores  30  40  50  60  70  80 
No. of Players  4  11  17  12  10  6 
CONTINUOUS SERIES
Q.1 COMPUTE LOWER QUARTILE AND UPPER QUARTILE FROM THE FOLLOWING DATA:  
ONLINE TRANSACTION (RS.)  Below
1,500 
1,500 – 3,000  3,000 – 4,500  4,500 – 6,000  6,000 – 7,500  7,500 & Above 
NO. OF CUSTOMERS  21  10  13  7  10  14 
Multiple Choice Questions:
Q.1 The ________ is that value of the variable which divides the group into two equal parts. 
a. Mean b. Mode c. Median d. Both (a) and (c) 
Q.2 Which of the following is merits of Median value of data? 
a. Easy To Calculate And Simple To Understand b. Rigidly Defined c. Not affected by extreme values d. All of the above 
Q.3 Which of the following is demerits of Median value of data? 
a. Arrangement of data is mandatory b. Affected by fluctuation in Sampling c. Lack of further algebraic treatment d. All of the above 
Q.4 Median _______ extreme values. 
a. includes b. does not includes c. rejects d. None of the above 
Q.5 Median is not dependent upon which of the following criteria? 
a. All observations b. Extreme values c. Least values d. All of the above 
Answer Key 
1a, 2d, 3d, 4b, 5d 
The above mentioned is the concept, that is elucidated in detail about the ‘Measures of Central Tendency – Median ’ for the class 11 Commerce students. To know more, stay tuned to BYJU’S.