 # Measures of Central Tendency - Mode

The measure of central tendency mode is the value that appears regularly in the data set. On a histogram or a bar chart, the highest bar in the chart is the mode. In the data set if the data has multiple values and has occurred multiple times then the data has a mode. If the data have no value repeats than it does not have a mode.

Typically, the mode is used with ordinal, category, and discrete data. Also, the mode is only the measure that uses category data- for instance, the most liked flavored ice-cream. But, the category data doesn’t have a central value because it is not possible to order the group. However, the ordinal and discrete data has a mode with value and which is not in the center. In simple words, mode represents the most common value.

## Meaning, Merits and Demerits of Mode

 (A) MODE Mode is that value which occurs most frequently in a distribution. It is the most common value found in a series. It is that value of the variable which has the highest frequency. (B) FOLLOWING ARE SOME OF THE MERITS OF MODE: (1) EASY TO CALCULATE & SIMPLE TO UNDERSTAND It is very easy to calculate. In some cases it can be determined just by observation or inspection. Everyone understands the concept of majority. Mode is based on this concept so, it’s easy to understand. (2)REPRESENTATIVE VALUE It is a value around which there is maximum concentration of observations. Hence, it can be considered as the best representative of the data. (3) NOT AFFECTED BY THE VALUE OF EXTREME ITEMS It is not affected by extreme values of the given data. It can be calculated even if these extreme observations are not known. (4) NO NEED OF COMPLETE DATA We can find mode even in case of open ended frequency distribution. We basically need the point of maximum concentration of frequencies, it is not necessary to know all the values. (5) USEFUL FOR BOTH QUANTITATIVE & QUALITATIVE DATA It can be used to describe quantitative as well as qualitative data. For example: In the surveys it is used to measure taste and preferences of people for a particular brand of the commodity. (6) GRAPHIC DETERMINATION It can be determined graphically with the help of Histogram. (C) FOLLOWING ARE THE SOME OF THE DEMERITS OF MODE: (1) NOT BASED ON ALL THE OBSERVATIONS OF THE SERIES The value of mode is not based on each and every item of the series as it considers only the highest concentration of frequencies. (2) SOMETIMES IT IS INDETERMINATE OR ILL DEFINED Value of mode may not be determined always. Some distributions can be Bi-modal, Tri-modal or Multi-modal. (3) NOT RIGIDLY DEFINED There are two methods of determining mode, Inspection Method and Grouping Method. We may not get the same value of mode by the two methods. So, it is not rigidly defined. (4) AFFECTED BY THE FLUCTUATIONS OF SAMPLING Mode is affected by sampling fluctuations to a great extent. This effect is more than that in case of Mean. (5) COMPLEX GROUPING PROCESS Grouping of data is desirable for correct computation but it is a complex process and involves so much calculations. (6) NOT CAPABLE OF ALGEBRAIC TREATMENT Since it is not based on all the observations and not rigidly defined, it is not suitable for further algebraic treatment.

### Practice questions:

INDIVIDUAL SERIES

 Q.1 FROM THE FOLLOWING DATA RELATING TO THE HEIGHT OF 10 STUDENTS, FIND THE VALUE OF MODE. Height (in Cm.) 160 155 148 155 160 162 160 174 160 180 Q.2 FOLLOWING IS THE DATA OF MARKS OF THIRTY STUDENTS. YOU ARE REQUIRED TO FIND MODE: 35 47 95 67 67 95 57 76 75 75 80 67 76 75 50 86 75 80 99 75 33 65 67 57 65 75 76 86 80 76

DISCRETE SERIES

 Q.1 A SURVEY WAS CONDUCTED ON 250 PEOPLE HAVING 25 PERSONS EACH OF DIFFERENT AGE LEVEL TO ASSESS THE CASES OF DEPRESSION THAT REQUIRE COMPULSORY COUNSELING. OUT OF THESE 70 PERSONS WERE FOUND TO BE THE VICTIM OF THIS DISEASE. IT WAS DECIDED TO COMPUTE MODEL AGE FROM THE FOLLOWING FOR THIS PROGRAMME: Age (in Years) 60 65 70 75 80 85 No. of Cases of Depression 6 10 10 14 19 11 Q.2 FROM THE FOLLOWING DATA COMPUTE AVERAGE POCKET MONEY RECEIVED BY THE STUDENTS. (USE MODE): Pocket Money (X) 20 30 50 60 70 80 100 No. Of Students 8 14 17 15 10 5 20

CONTINUOUS SERIES – INSPECTION METHOD

 Q.1 FIND MODAL VALUE OF VARIABLE FROM THE FOLLOWING DATA: Variable 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 Frequency 4 9 20 25 20 8 6

CONTINUOUS SERIES – GROUPING METHOD

 Q.2 COMPUTE MODE FROM THE FOLLOWING DATA: Marks (X) 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 -70 No. Of Students 16 7 12 15 13 8 5 Q.3 COMPUTE MODE FROM THE FOLLOWING DATA: Mid Values 2.5 7.5 12.5 17.5 22.5 27.5 32.5 Frequency 2 3 15 12 15 14 8 Q.4 COMPUTE MODE FROM THE FOLLOWING DATA: (USE GROUPING METHOD) X 0 – 9 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79 f 2 7 12 17 14 15 9 4 Q.5 COMPUTE MODE FROM THE FOLLOWING DATA: (USE GROUPING METHOD) X Less Than 25 Less Than 40 Less Than 55 Less Than 70 Less Than 85 Less Than 100 f 6 21 33 46 54 55 Q.6 COMPUTE MODE FROM THE FOLLOWING DATA: (USE INSPECTION METHOD) X More than 0 More than 10 More than 20 More than 30 More than 40 More than 50 More than 60 f 100 90 75 55 27 11 5 Q.7 COMPUTE MODE FROM THE FOLLOWING DATA: (USE INSPECTION METHOD) X 0 – 8 8 – 12 12 – 20 20 – 30 30 – 40 40 – 60 60 – 75 75 – 80 f 2 7 6 4 8 30 10 3 Q.8 COMPUTE MODE FROM THE FOLLOWING DATA: (USE INSPECTION METHOD) X 0 – 10 20 – 40 40 – 50 50 – 80 80 – 90 f 10 16 12 27 10 Q.9 COMPUTE MODE FROM THE FOLLOWING DATA: (USE INSPECTION METHOD) Variable Below 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 90 & above Frequency 13 17 25 23 10 8 7

FINDING MODE IN CASE OF BI-MODAL, TRI-MODAL & MULTI-MODAL SERIES

 Q.1 FROM THE FOLLOWING LOCATE THE VALUE OF MODE: Age (in Years) 15 16 16 15 17 18 16 17 17 15 18 Q.2 IF ARITHMETIC MEAN OF A DISTRIBUTION IS 45 AND MEDIAN VALUE IS 47.5. WHAT WILL BE THE VALUE OF MODE?

LOCATING MODE GRAPHICALLY

 Q.1 FROM THE FOLLOWING LOCATE THE VALUE OF MODE: X 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 f 20 30 50 80 30 15 5
 Q.1 __________ is that value which occurs most frequently in a distribution. a. Mean b. Median c. Mode d. None of the above Q.2 Which of the following is a merit of calculating mode? a. Easy to calculate b. Simple to understand c. No need of complete data d. All of the above Q.3 Which of the following is a demerit of calculating mode? a. Not based on all observation b. Not rigidly defined c. Complex grouping process d. All of the above