Tally marks is an interesting and simple topic of statistics. Generally, tally marks and graphs are used to keep and count the score. Symbol '|' is used to represent the value one. Here, we will cover the topic of tally marks and graphs. In olden days, before the discovery of the numbers, it was very hard to keep track of the personal belongings of people, e.g., humans used to have domestic animals such as goats and cows, and keeping track of their count was very hard if the number was very large. At that time, tally marks were very helpful.

Tally marks can be defined in the unary numeral system. It is a form of numeral which is used for counting. The general form of writing tally marks is as a group or set of five lines. The first four lines are drawn vertical and each of the fifth line runs diagonally over the previous four vertical lines, i.e., from the top of the first line to the bottom of the fourth line. Tally mark is the quickest way of keeping track of a group of five.
Tally marks are the quickest way of keeping track of numbers in groups of five.

### Solved Example

**Question: **Lets check the table below and try to answer all the questions connected with it.

1. Which item has the largest count?

2. Which two items have the same count ?

** Solution: **

1. Ball has the largest count of 13.

2. Both pencil and chair have the same count of 4.

### Solved Example

**Question: **

** Solution: **

Given below are some of the examples on tally marks. ### Solved Examples

**Question 1: **Lets consider the marks of 25 students in standard IX in a particular school. The scores are as follows:

41, 53, 64, 31, 53, 33, 70, 61, 74, 32, 53, 56, 56, 64, 56, 88, 28, 70, 56, 64, 74, 53, 53, 61, 31.

The maximum mark allotted to the paper is 100. Draw a tally chart for the above data.

** Solution: **

Rearranged data in ascending order:

Using the tally mark table, different data can be obtained without actually going through the observations.

**Question 2: **Consider a garden with lots of flowers. Mary has different types of flower pots which are given in the table below:

Using this table, it's very easy to get different information, without actually going through the observations.

1. How many Daisy flower pots are there?

2. Which two flowers have the same number of pots?

3. Which flower has the maximum number of pots?

** Solution: **

1. It can be seen that there are two tally marks in front of the Daisy row. So the number of Daisy flowers pots is 2.

2. It can be seen that in front of Lily and Jasmine, the number of tally marks are 4. So both Lily and Jasmine has the same number of pots.

3. In the table, the maximum number of tally marks 10, can be seen only in the Tulip row. So, the Tulip has the maximum number of pots.

**Question 3: **The following raw data shows the heights of 40 students of a class division.

140, 156, 134, 152, 162, 148, 141, 147, 139, 147, 152, 144, 154, 133, 144, 153, 161, 149, 156, 137, 150, 146, 135, 142, 152, 148, 154, 138, 139, 157, 144, 147, 149, 139, 142, 155, 143, 131, 154, 146.

** Solution: **

The class limits should be fixed so as to include the least score 128 in the first class and the highest score 162 in the last class. This can be done as follows:

Tally marks give a good basis for small children who have started to learn about numbers. It gives them an idea of arranging and differentiating.

Here,

- The value 1 is represented by
**|**tally marks. - The value 2 one is represented by
**| |**tally marks. - The value 3 is represented by
**| | |**tally marks. - The value 4 is denoted by |||| tally marks.
- The value five does not denoted by | | | | | tally marks in the graphs. For the number 5, draw four vertical lines (||||) with a diagonal (\) line through it.

1. Which item has the largest count?

2. Which two items have the same count ?

Item |
Tally Marks | Total |

Pen | || | 2 |

Paper | || | 7 |

Pencils | |||| | 4 |

Ball | ||| | 13 |

Chalk | 5 | |

Chair | |||| | 4 |

1. Ball has the largest count of 13.

2. Both pencil and chair have the same count of 4.

Tally mark graph is a graphical representation of the data. It is very helpful to read the data very quickly. Tally marks in graphs are a quick way of keeping track of numbers in groups of five. Graph table has one vertical line which is made for each of the first four numbers and the fifth number is represented by a diagonal line across the previous four. Let us see with the help of example how to create a graph for the data written in tally form.

Take a survey of 10 friends. They will vote for their favorite instrument.

Flute | | |

Piano | || |

Drum | ||||| |

Guitar | ||| |

Keyboard | |||| |

- If you have | (one tally marks) then the flute count is the number 1.
- If you have || (two tally marks) then the piano count is the number 2
- If you have ||||| (five tally marks) then the drum count is the number 5
- If you have ||| (three tally marks) then the guitar count is the number 3
- If you have |||| (four tally marks) then the keyboard count is the number 4

Possible tally graph is shown below

41, 53, 64, 31, 53, 33, 70, 61, 74, 32, 53, 56, 56, 64, 56, 88, 28, 70, 56, 64, 74, 53, 53, 61, 31.

The maximum mark allotted to the paper is 100. Draw a tally chart for the above data.

Rearranged data in ascending order:

Using the tally mark table, different data can be obtained without actually going through the observations.

Using this table, it's very easy to get different information, without actually going through the observations.

1. How many Daisy flower pots are there?

2. Which two flowers have the same number of pots?

3. Which flower has the maximum number of pots?

1. It can be seen that there are two tally marks in front of the Daisy row. So the number of Daisy flowers pots is 2.

2. It can be seen that in front of Lily and Jasmine, the number of tally marks are 4. So both Lily and Jasmine has the same number of pots.

3. In the table, the maximum number of tally marks 10, can be seen only in the Tulip row. So, the Tulip has the maximum number of pots.

140, 156, 134, 152, 162, 148, 141, 147, 139, 147, 152, 144, 154, 133, 144, 153, 161, 149, 156, 137, 150, 146, 135, 142, 152, 148, 154, 138, 139, 157, 144, 147, 149, 139, 142, 155, 143, 131, 154, 146.

The class limits should be fixed so as to include the least score 128 in the first class and the highest score 162 in the last class. This can be done as follows:

Tally marks give a good basis for small children who have started to learn about numbers. It gives them an idea of arranging and differentiating.

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