Tally numeration system

The tally numeration system is probably the simplest of all numeration systems ever used.It makes use of single strokes to represent objects that are being counted. One stroke is used for each object.

Tally numeration
The figure above shows how we can use stroke(s) to represent the count for 1, 2, or 3 squares.

Disadvantages of the tally numeration system.


Although one advantage is simplicity, there are two disadvantages.
  • First, large number will require an awful lots of strokes.
  • Second, it will be somewhat difficult to read such large number.

For example, can you tell what number is represented by the tally marks below?

Tally numeration of 20


I know what you are doing right now. You are using your finger to count the strokes perhaps.

However, would you be able to do that without confusing yourself or losing your place if there were 50 strokes? How about 1000 strokes? With 1000 strokes, perhaps you will not even bother yourself counting the number of strokes.

Anyway, if you did not lose your place when trying to count the number of strokes in the figure above, you must have counted 20 strokes.

How grouping made it a little easier to read numbers in the tally numeration system.

The introduction of grouping made it a lot easier to read numbers.

In this case, we place a fifth tally mark across every four strokes to make a group of 5.

The number shown above will be represented as follow:

Tally numeration of 20


Did you notice that you were able to find the number a lot faster?

Basically, that is all there is to this numeration system.Today, this numeration system is used a lot in statistics.

How the tally numeration system is used in statistics.

A sample was taken of 30 high school students who were planning to go to college after graduation. The students had 5 choices.

  1. Mathematics
  2. Computer Science
  3. Business
  4. Pre-Med
  5. Other

The responses of the students are shown below:

Other      Business      Mathematics       Other      Mathematics 

Computer Science    Pre-Med    Business   Other  Business

Mathematics  Other   Computer Science   Pre-Med

Computer Science  Business   Other  Business   Other

Mathematics  Business  Pre-Med  Computer Science   Business

Business  Computer Science  Other   Business    Business  Other  

Construct a frequency table using the tally numeration system.

To make a frequency table, use a table that has 3 columns and 6 lines. The first column on the left will have the 5 different majors. The second column in the middle will have tally marks. The last column will show the frequency as a number. 

Read each student's response from the data above and mark a tally. 

Here is what the table should look like.

How the tally numeration system is used in statistics

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