Tally chart
A tally chart is a method to present information where the data is recorded using different sets of vertical dashes. A single dash signifies the counting of a single item.
Every time an object is observed or counted a dash is drawn next to the previous dash till the number of dashes reaches four.
When the counted number of items crosses five, four dashes are followed by a diagonal dash that cuts across the four lines that were previously drawn.
Bar graphs
Another way to present information is using bar graphs. In this case, different rectangular bars are placed side by side. Each bar signifies different items that are considered. The length of each bar signifies the repeated number of each item.
Picture chart
A picture chart is another method of displaying data. Here we see a picture that represents a particular object. As the number of objects increases, so does the picture depicting the same.
What are the uses of Representing Data?
We can display data in different forms to allow easy interpretation of information. Numbers are usually in the form of symbols. A person who views the numbers cannot understand them in comparison to other values. When using data representations like the ones we talked about like tally marks, bar graphs and picture graphs, we can easily view and compare the different values.
Any of these forms of data representation can be used at any point in time.
A class of students was asked what they aspired to become when they grew up. The teacher recorded their responses in the form of tally marks, a bar graph as well as in the form of a picture chart. Here’s what the representations looked like.
Tally marks:
Bar Graph:
Picture chart:
Solved Examples
Example 1: Given below is a table that has the tally scores of the favorite pets of a set of students.
- Among the three pets, which pet is most preferred by the majority of the class?
- Which is the pet that was chosen least often as the favorite pet?
Solution:
The pet that is most often chosen as the favorite pet of the students is the cat. Ten students chose the same.
The pet that is chosen as the favorite by the least number of students is the dog. Four students chose the dog as their favorite animal.
Example 2: The students of a class of 25 students enrolled for a few activities. The remaining students are to be enrolled in the archery club.
- Find the number of students to be enrolled in the archery club. Depict the same in the blank column given below.
- From the table, which is the least picked activity.
Solution:
There are a total of 25 students.
The number of students that enrolled in the activities given above = 4 + 7 + 3 + 4 = 18
The number of students that will be enrolled in the archery club = 25 – 18 = 7
The club that is least preferred is the sculpture club.
Example 3: A fast-food restaurant was asked to make a list of the food items sold on a particular day.
- Which food item is the most preferred?
- How many food items of the lesser preferred ones should be added to match up to the number of the most preferred food item sold?
Solution:
Pizza is the most preferred food item. Nine pizzas were sold on that day.
For the french fries to match up the number of the pizzas sold we deduct the total number of the french fries sold from the total number of pizzas.
7 – 6 = 1
So, one more set of french fries should be added to the existing number to match up to the number of pizzas that were sold on that day.
For the burgers to match up to the total number of pizzas, deduct the total number of burgers from pizzas.
7 – 3 = 4
So, this means that three burgers should be added to the total number of burgers to match up to the number of pizzas that were sold on that day.
All the three forms of data representation, tally charts, bar graphs, and picture graphs, are useful according to the need and the how immediately the data is needed. For example, the tally marks are useful where the observations need to be recorded spontaneously. The bar graph or the picture graph is used when a visual representation of some data already collected is required.
Imagine a scenario where you are asked to count the number of balls that are being dropped from a place of height. In this scenario where the action is happening simultaneously, using a single line to represent each ball is more convenient than writing down a list of numbers.