Tally Marks and Frequency Table
Suppose your teacher asks the class about their favourite fruit. Students call out their answers: Mango, Apple, Mango, Banana, Mango, Apple... How do you keep count without losing track? You use tally marks!
Tally marks are a simple way to count things one by one. You make a short vertical line for each item, and every fifth mark crosses the previous four, making groups of 5 that are easy to count.
A frequency table organises this data neatly, showing each item and how many times it appeared (its frequency).
What is Tally Marks and Frequency Table - Grade 6 Maths (Data Handling)?
Definition:
- Tally marks: Short vertical lines (|) used to count items. Every 5th mark is drawn diagonally across the previous 4, making a bundle of 5.
- Frequency: The number of times a particular item or value appears in the data.
- Frequency table: A table that lists each item (or value) along with its frequency.
How tally marks work:
- 1 = |
- 2 = ||
- 3 = |||
- 4 = ||||
- 5 =
||||(four vertical lines with a diagonal line crossing them) - 6 =
||||| - 7 =
||||||
Tally Marks and Frequency Table Formula
Steps to make a frequency table:
- List all the different items (or values) in the data.
- Go through the data one item at a time.
- For each item, make a tally mark next to it.
- After going through all the data, count the tally marks for each item.
- Write the count in the frequency column.
- Check: The sum of all frequencies must equal the total number of data items.
Types and Properties
Uses of frequency tables:
- Ungrouped frequency table: Lists individual values and their frequencies. Used when data values are few and distinct. Example: favourite colours of students.
- Grouped frequency table: Groups values into ranges (called class intervals) when there are many different values. Example: marks ranging from 0 to 100 grouped as 0-10, 10-20, etc. (This is covered in detail in higher classes.)
Parts of a frequency table:
- Column 1: Item or value
- Column 2: Tally marks
- Column 3: Frequency (count)
Solved Examples
Example 1: Making a Frequency Table for Favourite Fruits
Problem: 20 students chose their favourite fruit: Mango, Apple, Mango, Banana, Mango, Apple, Grapes, Mango, Banana, Apple, Mango, Grapes, Mango, Apple, Banana, Mango, Apple, Mango, Grapes, Banana.
Make a frequency table.
Solution:
- Mango:
||||||| = 8 - Apple:
||||= 5 - Banana: |||| = 4
- Grapes: ||| = 3
Check: 8 + 5 + 4 + 3 = 20. Correct!
Example 2: Frequency Table for Dice Rolls
Problem: A dice is rolled 15 times. Results: 3, 5, 2, 3, 6, 1, 3, 4, 2, 5, 3, 1, 6, 4, 2. Make a frequency table.
Solution:
- 1: || = 2
- 2: ||| = 3
- 3: |||| = 4
- 4: || = 2
- 5: || = 2
- 6: || = 2
Check: 2 + 3 + 4 + 2 + 2 + 2 = 15. Correct!
Example 3: Reading a Frequency Table
Problem: A frequency table shows: Red = 7, Blue = 5, Green = 3, Yellow = 5. (a) Which colour is most popular? (b) How many students were surveyed?
Solution:
(a) Red has the highest frequency (7), so it is most popular.
(b) Total = 7 + 5 + 3 + 5 = 20 students.
Example 4: Converting Tally Marks to Numbers
Problem: Convert these tally marks to numbers: (a) |||| || (b) |||| |||| ||| (c) ||||
Solution:
- (a)
|||||| = 5 + 2 = 7 - (b)
||||||||||| = 5 + 5 + 3 = 13 - (c) |||| = 4
Example 5: Finding the Mode from a Frequency Table
Problem: From the frequency table: Score 1(3 times), 2(5 times), 3(7 times), 4(4 times), 5(1 time). What score appeared most often?
Solution:
Score 3 has the highest frequency (7).
Answer: The score that appeared most often is 3 (this is also called the mode).
Example 6: Frequency Table for Transport Modes
Problem: How students come to school: Bus, Walk, Bus, Car, Bus, Walk, Car, Bus, Walk, Bus, Bicycle, Bus, Walk, Car, Bus. Make a frequency table.
Solution:
- Bus:
|||||| = 7 - Walk: |||| = 4
- Car: ||| = 3
- Bicycle: | = 1
Check: 7 + 4 + 3 + 1 = 15. Correct!
Example 7: Drawing Tally Marks for 23
Problem: Represent the number 23 using tally marks.
Solution:
23 = 4 groups of 5 + 3 more
|||| |||| |||| |||| |||
Check: 5 + 5 + 5 + 5 + 3 = 23. Correct!
Example 8: Checking the Total Frequency
Problem: A class of 30 students voted for their favourite sport. The frequency table shows: Cricket = 12, Football = 8, Badminton = 6, Tennis = 3. Is the table correct?
Solution:
Total = 12 + 8 + 6 + 3 = 29.
But the class has 30 students.
Answer: The table is incorrect. One student's vote is missing. The sum of frequencies must equal 30.
Real-World Applications
Where tally marks and frequency tables are used:
- Voting and surveys: Counting votes in class elections, customer surveys.
- Inventory: Shopkeepers count items in stock using tally marks.
- Sports: Keeping score by making a mark for each point.
- Science experiments: Recording results of repeated experiments (like dice rolls or coin tosses).
- Traffic surveys: Counting the number of cars, buses, and bikes passing a point.
- Weather: Recording the number of sunny, rainy, and cloudy days in a month.
Key Points to Remember
- Tally marks are vertical lines used for counting. Every 5th mark crosses the previous 4.
- Frequency is the number of times an item appears.
- A frequency table has columns for item, tally marks, and frequency.
- The sum of all frequencies must equal the total number of data items.
- Tally marks make counting large amounts of data easier and less error-prone.
- Frequency tables organise raw data into a clear, readable format.
- The item with the highest frequency is the mode.
Practice Problems
- Represent 17 using tally marks.
- Survey 10 classmates about their favourite subject. Make a frequency table.
- A frequency table shows: Cat = 6, Dog = 9, Fish = 3, Bird = 2. How many people were surveyed? Which pet is most popular?
- Convert: (a) ||||| |||| to a number, (b) 14 to tally marks.
- A class has 25 students. The frequency table shows scores: A=8, B=6, C=5, D=4. Is data missing?
- Roll a dice 20 times and record the results in a frequency table.
Frequently Asked Questions
Q1. What are tally marks?
Tally marks are short vertical lines used to count items. You draw one line for each item. Every fifth line is drawn diagonally across the previous four, making a group of 5 for easy counting.
Q2. Why do we cross the fifth tally mark?
Crossing the fifth mark creates groups of 5. This makes it much easier to count large numbers. Instead of counting individual lines, you count groups of 5 and add the remaining lines.
Q3. What is a frequency table?
A frequency table is a table that shows each item or value in the data along with how many times it appears (its frequency). It usually has three columns: item, tally marks, and frequency.
Q4. What is frequency?
Frequency is the number of times a particular value or item appears in a data set. For example, if 8 students chose mango as their favourite fruit, the frequency of mango is 8.
Q5. How do I check if my frequency table is correct?
Add all the frequencies together. The total must equal the total number of data items. If it does not match, you have missed or double-counted something.
Q6. What is the difference between data and frequency?
Data is the raw information collected (the actual responses or measurements). Frequency is the count of how many times each value appears in the data.
