What is Data?
Data is generally defined as a collection of information containing numbers and words. Data is collected by observation, counting and measurement.
What is the Difference between Grouped Data and Ungrouped Data?
When data is collected and organized or sorted into groups, we call it grouped data. A list of students who like different sports sorted by the name of the sport, is an example of grouped data. When data is not organized or sorted into groups, we call it ungrouped data. The score of 10 students for an exam is an example of ungrouped data.
What is a Tally chart?
A tally chart is a table used to keep a record of the count of things. A tally chart contains tally marks — a series of lines that represent numbers. Tally charts are often used to record scores, marks, a count of things, and much more.
How do we Represent Numbers using Tally Marks?
Tally marks are represented by five lines: four vertical lines and a diagonal line. The four vertical lines are used to count up to four. The fifth of the count, is recorded using a diagonal line which is a line drawn across the four vertical lines.
These lines are repeated for bigger numbers. Check out the table to learn how numbers are represented using tally marks.
In a tally chart, tally marks are used to represent five counts at a time. Numbers higher than 5 are represented by repeating the same pattern of tally marks. For example, 14 is represented as 5 + 5 + 4.
What is the Purpose of using Tally Marks?
Before the number system was developed, it was not possible to express a number using a symbol as we do now. Ancient people did not know how to use numbers to count things, like the number of animals they had hunted in a week. People used to count things with the help of engravings on the surfaces of rocks and bones. Tally marks were developed specifically to serve this purpose of counting.
Why are Tally Marks Grouped into sets of 5?
Since tally marks are represented in groups of 5, it was easy for people to comprehend the numbers. Without the grouping of tally marks into five, it would be difficult to count the number of straight lines. For example, 14 would be represented as
Expressing numbers in this manner would make it difficult for people to comprehend. This is why grouping tally marks into 5 is important.
In tally marks, a diagonal line is used to show that the count has reached 5. By knowing the number of fives, it is easy to add up the count to find the number it represents. By grouping tally marks into 5, we can represent 14 as
Solved Examples
Example 1:
Joe’s father asked him to count the number of sheep in the flock and the number of hens in his chicken farm. He created a tally chart to count the number of sheep and hens. Joe’s father was expecting him to count 14 sheep 18 hen. Observe the tally chart to find the number of missing animals.
Solution:
We can find the number of missing animals using Joe’s tally chart.
Actual number of sheep = 14
Actual number of hen = 18
Number of sheep according to the tally chart = 12
Number of hens according to the tally chart = 17
Number of sheep that have not been counted = 14 – 12 = 2
Number of hens that have not been counted = 18 – 17 = 1
Therefore, there is a total number of three farm animals that have not been counted.
Example 2:
Nikita conducted a survey among 15 friends and recorded their favorite sports. The observations are as follows:
a. Prepare a tally chart for the observations.
b. Which sport is most popular among Nikita’s friends?
c. Which sport is least popular among Nikita’s friends?
Solution:
a. The tally chart can be made by counting the number of friends who like each sport.
b. As we can see from the tally chart, basketball is the most popular sport among Nikita’s friends.
c. The least popular sport among Nikita’s friends is soccer.
Example 3:
Jack and Angela played a game of counting vehicles while they were walking back home. Jack kept a count of the buses and trucks and Angela kept a count of the cars on the road. Each count gives the player one point. The person who has the highest points when they reach home wins the game. Their observations are shown below.
a. Who won the game?
b. By how many points did the winner win the game?
c. If Jack missed out on counting three buses, what would the tally chart look like?
Solution:
a. Let’s answer all these questions!
Number of vehicles counted by Jack =
= 5 + 5 + 4 = 14
Number of vehicles counted by Angela =
= 5 + 5 + 5 + 5 + 3 = 23
Angela won the game because she counted more vehicles, as indicated by the tally marks.
b. Difference between Angela and Jack’s points = 23 – 14 = 9 points
c. If Jack missed out on counting three buses, the original count would be 17. The equivalent tally marks are = 5 + 5 + 5 + 2 =
Example 4:
Carla’s teacher asked her to conduct a survey among 30 students to find the number of students who would like to take part in activities like dramatics, music, dance, and painting. Her observations are given below.
How many more students should Carla approach to achieve her target?
Solution:
To find the number of students Carla has to approach to achieve the target, we need to find the number of students she has already approached. Let’s convert the tally marks into numbers.
The total number of students Carla has already approached = 8 + 7 + 6 + 5 = 26
Number of students she has to approach = 30
Number of students she is yet to approach = 30 – 26 = 4 students
We use a diagonal line in tally marks when the count goes up to 5. This method of representing numbers makes it easier for a person to comprehend the total count.
Tally marks are not as effective as the number system that we use today in terms of simply representing numbers. But tally marks can be useful for noting down observations while performing activities or experiments.
Math operations like addition and subtraction can be carried out easily with tally marks. We just need to add or subtract the number of lines from the original tally marks.