Tally Chart: Definition, Counting Tally Mark Using Chart with Examples

Tally Marks are a part of the unary numeral system. They are used globally for counting and for a visual representation of grouped observations. Tally mark or hash mark is a very easy and commonly used way of representing scores in various sports. The tally mark is represented by a symbol “|” (single verticle bar) to indicate one. Tally charts are used to collect data using tally marks. It is a quick and efficient way of data collection as filling a chart with tally marks is much faster than writing words. Tally charts can also be used for solving operations involving addition, subtraction, or word problems.

This article will provide students will all the details about Tally Charts and Tally Marks including definitions, uses, and benefits. Students will also be able to learn how to represent data using tally marks with provided solved examples. Read on to learn more.

Tally Marks Definition

Tally marks are the numerical system that makes counting easier. Tally means equal, or that matches the counting of a particular object or thing. They can count the points, people, score etc., Though the tally mark differs from one country to another, the general way of writing a tally mark is set of five lines. One vertical line means count \(1\). Four vertical lines mean \(4\), while four vertical lines and a line across the four lines mean \(5\).

Tally marks are the quick way of monitoring the numbers in groups of five. The table below shows the counting from \(1\) to \(10\). Let us understand the logic in the counting numbers and tally marks used to represent them.

From the above table, we observe that

1. One vertical line representing count \(1\)-
2. Two vertical lines representing count \(2\)-
3. Three vertical lines representing count \(3\)-
4. Four vertical lines representing count \(4\)-
5. Four vertical lines and a line drawn across four vertical lines representing count \(5\)-
6. Set of five lines and a single vertical line representing count \(6\)-
7. Set of five lines and two single vertical lines representing count \(7\)-
8. Set of five lines and three single vertical lines representing count \(8\)-
9. Set of five lines and four single vertical lines representing count \(9\)-
10. Two sets of five lines representing count \(10\)-

Tally Mark Chart

In statistics, a graphical representation of the data uses a tally mark chart. It helps us in arranging the data in a clear view. Tally marks on graphs are a quick way to track numbers in groups of five. A group of tally marks showing data information in a table produce a tally chart.

A tally chart is shown below consisting of tally marks for the numbers counting from \(1\) to \(10\).

Benefits of Using Tally Marks

Assume that we are given raw data or random values to formulate a frequency distribution. We have options to make an individual observation or class intervals. It is difficult to count all the occurrences and enter the data as there are chances of mistakes. Also, going back to the list repeatedly to cross-check the entire list becomes time-consuming. This complication can be minimized by using the tally marks.

In this case, we have to add a tally mark for every different observation or class interval. In this way, we have to pass over the list only once. Then by counting the tally marks, we can write down the corresponding frequencies. Thus, the table obtained is the required frequency distribution table for the given data.

This is how the tally marks become beneficial for finding the frequencies of the data set, particularly for ungrouped raw data. The below example helps us understand the concept in a better way.

Example: Let us assume you decided to make a tally chart to show marks of your classmates out of \(5\). Recording it using numbers every time, you have to erase the previous data and write the new one. So using tally marks becomes easier for you to record the data.

To look through this chart, you need to count the tally marks to find the number of students.

1. First is the number of students getting \(1\) mark. One of your classmates has got \(1\) mark, so you draw one tally mark in front of it.
2. Second is the number of students getting \(2\) marks. Four of your classmates got \(2\) marks, so you make four tally marks next to it.
3. The third is the number of students getting \(3\) marks. Six of your classmates got \(3\) marks, so you make a set of five tally marks and a single tally mark next to it.
4. Fourth is the number of students getting \(4\) marks. Eight of your classmates got \(4\) marks, so you make a set of five tally marks and three single tally mark next to it.
5. Fifth is the number of students getting \(5\) marks. One of your classmates got \(5\) marks, so you make one tally mark next to it.

Including you, your class strength is \(20\). So the tally mark to show the total number of students is \(=20\) tally marks.

Solved Examples – Tally Chart

Q.1. The height of the students in cm from grade \(8\) is listed below:
\(127,112,120,124,123,127,117,126,127,117,123,128,132,113,124,129,112,124,\)
\(130,116,133,118,121,129,116,123,133,115,121,\)
\(135,122,120,116,122,134,123,118,122\)
Draw a frequency table using tally marks.
Ans: The following table represents the frequency distribution using tally marks:

Q.2. Teena listed the number of siblings for each of her friends in her class with the following results:
\(0,1,3,5,3,4,0,1,0,3,1,2,1,0,1,5,4,2,1,3,2,1,0\)
Make a tally of Teena’s results. How many friends had no siblings?
Ans: The following tally chart shows the number of siblings for each of Teena’s friends:

From the above tally chart, \(5\) of Teena’s friends did not have siblings.

Q.3. Tarun participated in thirty different quizzes with ten questions each. The number of answers he got correct in each quiz was as follows:
\(4, 2, 6, 8, 3, 5, 5, 3, 6, 6, 7, 4, 8, 8, 3, 10, 4, 7, 9, 5, 4, 9, 7, 6, 3, 4, 4, 5, 3, 6\)
Make a tally of Tarun’s results. In how many quizzes did he score \(8\) or more?
Ans: The following table represents the tally chart for the given data:

From the above tally chart or frequency table, we can observe that Tarun scored \(8\) in \(3\) quizzes, \(9\) in \(2\) quizzes and \(10\) in \(1\) quiz. So total quizzes he scored \(8\) or more \(=3+2+1=6\).

Q.4. Soniya recorded the vowels (a, e, i, o and u) from a page of her textbook, with the following results:
\(a, e, e, i, o, a, a, e, e, o, o, e, e, a, u, o, i, e, e, a, i, u, i, e, a, u, e, a, a, e, e, a, a, o, e, a, e, i, o, e\)
Tabulate a tally chart of Soniya’s results. How many of the letter “\(e\)” did she get?
Ans: The tally chart is tabulated for the given data as follows:

From the tally chart, we observe that Soniya got \(15\) “\(e\)” letters.

Q.5. Water bottles are filled using a cup. The water-filled (in ml) in each bottle is listed below. 
\(777, 756, 780, 785, 768, 759, 773, 770, 765, 779, 782, 796, 780, 795, 776, 752, 758,790,\)
\(797, 796,780, 799, 777, 784, 789, 790, 785, 763, 759, 781, 755, 786, 762, 769,751, 780,\)
\( 754, 752, 769, 773, 760, 758, 799, 793, 752, 768, 789, 800, 772, 762, 751,785, 788, 778\)
Draw tally marks for the given data.
Ans: The tally mark is drawn for the given data as follows:

Summary

In this article, we have done a detailed study of the tally chart. We learnt the definition of the tally mark and then the counting of the tally mark. Then we explained how a tally mark chart could be prepared and read. We understood the importance and benefits of adopting a tally mark chart. Further, for better understanding the idea of the tally chart, examples have been solved for students.

Learn the Concepts on Data Representation

Frequently Asked Questions (FAQs) – Tally Chart

Q.1. What is a frequency distribution?
Ans: A frequency distribution is the data tabulated in a table using tally marks for various observations. The number of times an observation occurs is called the frequency. Tally marks indicate the number of times observation is repeated, and the frequency is thus written.

Q.2. What is the tally chart?
Ans: Tally charts are recordings that categorize the given data in an organized way. They are much more accessible and efficient. They give us the frequencies of each category. Further, the data can be represented on a bar graph.

Q.3. How do you make a tally chart?
Ans: For any given raw data, we have to make categories and then show each occurrence by a tally mark, and every fifth tally is drawn diagonally on the previous four tally marks. Then the tallies are counted to find the frequencies.

Q.4. What is the tally mark of 5?
Ans: Tally mark of five is called a set of \(5\) in which four vertical lines are drawn and a diagonal line in cross direction drawn on the last four lines. It is also considered as one group in tally marks. It is indicated as .

Q.5. What is the difference between a tally chart and a tally mark?
Ans: A tally chart is a table with tally marks to show a valuable set of data. A tally chart is one method of collecting data with tally marks. Tally marks are frequencies, occurrences, or total numbers measured for a specific group in a set of data.

We hope this detailed article on the tally charts helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!