Tally Marks

Before numbers were invented people found it difficult to keep records of their belongings and hence they used to do counting by sticks which are further known as tally marks. Tally marks, or hash marks, are a form of the unary numeral system used for counting. Tally marks are most commonly used to represent the scoreboard in games and sports. A frequency of data can be easily represented using Tally marks.

Tally marks are denoted by a single vertical bar ‘ | ‘.

Here are 1 to 4 counting numbers represented in tally marks:

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Tally records counting using a mark ‘|’. You may use the tally method to solve addition, subtraction, or word problems.

Tally Marks Definition

Tally marks are a way to mark or record your counting. Tally marks are a numerical system used to make counting easier. As the name suggests, it is a system that helps keep the “tally” of things by number. Tally marks are commonly used for counting scores, points, number of people, etc. Tally marks differ from country to country, as each culture has developed its own systems.

The general way of writing tally marks is four lines drawn vertically and the fifth line runs across the previous four vertical lines, i.e., from the top of the first line to the bottom of the fourth line. Then continue with the single lines again Tally mark is the set of five lines. Set of five lines are expressed as below:

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The sixth line will be written in this way-

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Counting Tally Marks

Let us understand how to use tally marks for counting 1 to 10 numbers. Here are the counting numbers and the tally marks representing them.

• One is expressed by ‘|’ tally marks.

• Two one is represented by ‘| |’ tally marks.

• Three is represented by ‘| | |’ tally marks.

• Four is denoted by ‘||||’ tally marks.

• Five is not denoted by five ‘| | | | |’ tally marks. For the number 5, draw four vertical lines (||||) and a line across the four lines (\). It is represented as

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• The sixth line is written as a single mark after a set of five lines, represented as ‘(Image to be added soon)|and similarly, you can continue.

• And then the tenth line is represented as 

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Tally Mark Chart

In statistics, a tally mark chart or graph is used for a graphical representation of the data. It helps us in organising data in a clear view. Tally marks on graphs are a quick way of keeping track of numbers in groups of five. When you see lots of tally marks showing data information in a table, you have a tally chart.

Let's look at an example of how to read and interpret tally charts.

For Example:

Let's say you decided to make a tally chart to show what your and your friend’s favourite type styles of candy are. If you record it by using numbers every time you have to erase the previous data and write the new one. So instead of using numbers, you use tally marks.it will become easier for you to record the data.

To read this chart, all you have to do is count how many tally marks are there next to each type of candy.

• First is ‘Chocolate Bars’ six of your friends like it so you will first write the set of five tally marks and then one tally mark. In this way you will write six tally marks.

• The second candy is  'Fruit-Flavored Hard Candy,' four of your friends like this type of candy so you make four tally marks next to it.

• The third is 'Chocolate with Caramel Inside,' 2 of your friends like this type of candy so there are 2 tally marks.

• Next is 'Butterscotch-Flavored Chews,'3 of your friends like this type of candy, so there are 3 tally marks.

• Next is 'None,' 1 of your friends doesn't like any of the candies listed, so write 1 tally mark.

If you take a look at the tally marks next to Chocolate Barslooksthe, you'll see they look a little different. Tally marks are grouped by 5. Once you get to the fifth tally mark, you must draw that one across the other tally marks like in the picture.

After the fifth tally mark, you need to start a new group.

This is what tally marks that show more than 5 looks like:

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  = 19 tally marks

Unicode Followed in the tally:

Ken Lunde and Daisuke Miura proposed in 2015 to encode some systems of tally markers with the Unicode standard. [9] Only five ideographic count characters (schemes) and two western count digits have been added to the Unicode standard for the Counting Rod Numerals block in Unicode version 11.0, with box tally characters and dot-and-dash tally characters encoded. Was not used for. (June 2018). Only the count marks for the numbers 1 and 5 are coded, and the count marks for the numbers 2, 3, and 4 must consist of a counting mark 1 sequence at the write level.

Fun Facts:

• The successive strokes of 正 (Image to be added soon) are used in China, Japan and Korea to represent tally marks.

• In France, Spain, South America, and some parts of Africa, instead of four vertical lines and a fifth diagonal one, they create a square with a diagonal through it (from upper right to bottom left).

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• Tally Using Dots and Lines

• Grouping these marks into five groups will improve readability. Draw one line for every first four counts, and the fifth count line intersects the previous four lines. The sixth count draws individual lines first. Many clone warriors have marked their helmets to indicate that they were killed during the Clone Wars. The 

•  A tally marker is primarily used to track a running tally. 

•  These markers help you track your game and sports scores. 

•  If you have a large amount of data, it is important to group them.

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There is another way to use tallying that is Tukey Tallying. But it is a little slower, as drawing dots takes a long time.

Uses of Tally Marks:

Tally marks are used when you are asked to take raw data or random numbers and generate a frequency distribution. In this situation, you may need to create individual observations or class intervals. If you want to mount all occurrences of a single data value or class interval at once, you need to check the following observations or a complete list of class intervals. Using counters can help simplify the situation. To achieve this, simply add a counter for each different observation or class interval. As a result,  the complete list of specified records needs to be repeated only once. Once the identification is complete, count the counters to get the frequency number. Therefore, the table created is called the frequency distribution table for the specified data. The tally mark is used this way to determine the frequency of setting data values, especially for ungrouped raw data. The sample questions resolved below will help you better understand this idea.

Key Terms:

• A collection of numbers is called data. They are collected and organized to provide some information. Raw data is information obtained in its original format. 

• Observed values ​​are raw data values ​​that differ from other data.

Data Types:

Data is collected based on inquiries or information needs. 

The data collected directly from the source is called the primary data. Imagine a situation where you need to collect information about a student's favourite game. You go to them and ask them directly. This is the most important information. 

Secondary data is data collected indirectly or from external sources. Newspapers, magazines, television, the Internet, and other media are examples of these sources. Suppose you need to collect information about the number of favourite restaurant locations in different cities. You can get your information from newspapers and the internet. This data is called secondary data.

Solved Examples

Example 1:

Rita recorded the vowels (a, e, i, o and u) from a page of her book, with the following results:

a, e, e, i, o, a, a, e, e, e, o, a, i, u, u, e, a, a, i, e, e, e, a, u, o, o, e, e, a, a, o, e, a, e, i, o, i, e, a, e

Make a tally of Rita's results.

How many more of the letter "e" did she get than the letter "u"?

Solution:

She got 15 e's and 3 u's.

So she got 12 more e's than u's.

Example 2:

John counted the different coloured cars that passed the school gate in five minutes with the following results:

Red, Black, Green, Red, White, Blue, Yellow, Red, Blue, White

Make a tally of John's results.

How many blue cars did he see?

Solution: 

He saw 2 blue cars.

Quiz Time

1. Daisy did a survey of the numbers of brothers and sisters for each of the children in her class with the following results:

0, 1, 5, 3, 6, 4, 0, 0, 1, 2, 3, 1, 0, 1, 5, 4, 2, 1, 3, 3, 2, 1, 0, 1

Make a tally of Daisy's results.

How many children had no brothers or sisters?

2. Earn sat thirty different quizzes with ten questions each. 

The number of questions he got correct each time were as follows:

4, 2, 6, 8, 3, 5, 5, 3, 6, 6, 7, 4, 3, 10, 5, 4, 9, 7, 6, 3, 8, 8, 4, 4, 5, 3, 6, 4, 7, 9

Make a tally of Ian's results.

In how many quizzes did he score 8 or more?