Mode
The mode is the value that appears most often in a data set. It is one of the three measures of central tendency (along with mean and median) that helps summarise a set of numbers with a single value.
Finding the mode is simple: look at the data, count how many times each value appears, and pick the one with the highest frequency. Unlike the mean, the mode does not require any calculation — just careful observation and counting.
The mode is especially useful for non-numerical data (like favourite colours or most popular sport), where calculating an average is not possible.
What is Mode - Class 5 Maths (Data Handling)?
The mode of a data set is the value that occurs with the greatest frequency (most number of times).
- A data set can have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal).
- If all values appear the same number of times, the data set has no mode.
Mode Formula
Mode = Value with the highest frequency
Steps to find the mode:
- Arrange the data (optional but helpful).
- Count the frequency of each value.
- The value with the highest frequency is the mode.
Types and Properties
Types of mode:
- Unimodal: One mode. Example: 2, 3, 3, 4, 5 → Mode = 3.
- Bimodal: Two modes. Example: 1, 2, 2, 3, 3, 4 → Modes = 2 and 3.
- Multimodal: More than two modes. Example: 1, 1, 2, 2, 3, 3 → Modes = 1, 2, and 3.
- No mode: All values appear equally. Example: 1, 2, 3, 4, 5 → No mode.
Solved Examples
Example 1: Example 1: Finding the Mode
Problem: Find the mode of: 5, 3, 7, 3, 5, 3, 8, 5, 3.
Solution:
Count frequencies: 3 appears 4 times, 5 appears 3 times, 7 appears 1 time, 8 appears 1 time.
Highest frequency: 3 (appears 4 times).
Answer: Mode = 3.
Example 2: Example 2: Mode of Test Scores
Problem: Marks of 10 students: 8, 7, 9, 8, 6, 8, 7, 9, 7, 8. Find the mode.
Solution:
6: 1 time, 7: 3 times, 8: 4 times, 9: 2 times.
Highest frequency: 8 (4 times).
Answer: Mode = 8.
Example 3: Example 3: Bimodal Data
Problem: Shoe sizes of students: 5, 6, 5, 7, 6, 8, 5, 6, 7, 5, 6. Find the mode.
Solution:
5: 4 times, 6: 4 times, 7: 2 times, 8: 1 time.
Both 5 and 6 appear 4 times each (highest).
Answer: Modes = 5 and 6 (bimodal).
Example 4: Example 4: No Mode
Problem: Find the mode of: 10, 20, 30, 40, 50.
Solution:
Each value appears exactly once. No value has a higher frequency than others.
Answer: This data set has no mode.
Example 5: Example 5: Mode of Favourite Colours
Problem: Ria surveys her class about favourite colours. Red: 6, Blue: 9, Green: 4, Yellow: 3. What is the mode?
Solution:
Blue has the highest frequency (9).
Answer: Mode = Blue.
Example 6: Example 6: Mode from a Frequency Table
Problem: A frequency table shows:
| Value | Frequency |
|---|---|
| 2 | 5 |
| 4 | 8 |
| 6 | 3 |
| 8 | 8 |
Find the mode.
Solution:
Values 4 and 8 both have frequency 8 (highest).
Answer: Modes = 4 and 8.
Example 7: Example 7: Mode of Cricket Runs
Problem: Arjun’s runs in 8 matches: 45, 32, 45, 60, 32, 45, 78, 32. Find the mode.
Solution:
32: 3 times, 45: 3 times, 60: 1 time, 78: 1 time.
Both 32 and 45 appear 3 times.
Answer: Modes = 32 and 45.
Example 8: Example 8: Mode vs Mean
Problem: Data: 10, 10, 10, 20, 50. Find the mode and the mean. Are they the same?
Solution:
Mode = 10 (appears 3 times).
Mean = (10 + 10 + 10 + 20 + 50) ÷ 5 = 100 ÷ 5 = 20.
Answer: Mode = 10, Mean = 20. They are not the same.
Example 9: Example 9: Finding Mode to Stock a Shop
Problem: A shoe shop records sizes sold in a day: 6, 7, 8, 7, 6, 7, 9, 7, 8, 6, 7. Which size should the shop stock the most?
Solution:
6: 3 times, 7: 5 times, 8: 2 times, 9: 1 time.
Mode = 7 (highest demand).
Answer: The shop should stock size 7 the most.
Example 10: Example 10: Mode of Dice Rolls
Problem: Dev rolls a dice 12 times: 3, 5, 2, 3, 6, 3, 1, 5, 3, 4, 5, 2. Find the mode.
Solution:
1: 1, 2: 2, 3: 4, 4: 1, 5: 3, 6: 1.
Highest frequency: 3 (appears 4 times).
Answer: Mode = 3.
Real-World Applications
Where do we use mode?
- Shopping: Shops stock the most popular (modal) sizes, colours, and products.
- Fashion: The most common dress size determines what factories produce most.
- Transport: The most frequently taken bus route gets more buses.
- School: The most common mark on a test tells the teacher what most students scored.
- Weather: The most frequent temperature in a month helps plan activities.
Key Points to Remember
- Mode = the value with the highest frequency in a data set.
- A data set can be unimodal (1 mode), bimodal (2 modes), multimodal (3+ modes), or have no mode.
- Mode works for both numerical and categorical data (numbers, colours, names).
- Mode does not require any calculation — just counting.
- Mode is different from mean (average) and median (middle value).
- Mode is useful for finding the most popular or most common item.
- Arranging data in order before counting makes it easier to find the mode.
Practice Problems
- Find the mode of: 4, 7, 2, 4, 9, 4, 7, 2, 4.
- The heights (in cm) of 8 plants are: 12, 15, 12, 18, 15, 12, 20, 15. Find the mode(s).
- Favourite fruits of 20 students: Mango (7), Apple (5), Banana (7), Orange (1). What is the mode?
- Data: 5, 10, 15, 20, 25. Does this data set have a mode?
- Runs scored by a player in 6 matches: 50, 40, 50, 30, 40, 50. Find the mode.
- A class votes for house captains. Aditi gets 12 votes, Rahul gets 15, Meera gets 12. What is the modal number of votes?
- Find the mode from this frequency table: Value 3 (freq 6), Value 5 (freq 9), Value 7 (freq 4), Value 9 (freq 9).
- Temperature recorded over 7 days: 32, 34, 32, 35, 34, 32, 33. Find the mode.
Frequently Asked Questions
Q1. What is the mode?
The mode is the value that appears most often in a data set. It is the most common or most frequent value.
Q2. Can a data set have more than one mode?
Yes. If two values share the highest frequency, the data is bimodal (two modes). If three or more share the highest, it is multimodal.
Q3. What if all values appear the same number of times?
If every value has the same frequency, the data set has no mode.
Q4. How is mode different from mean?
Mode is the most frequent value. Mean is the average (sum of all values divided by the count). They can be different numbers.
Q5. Can the mode be used for non-numerical data?
Yes. Mode is the only measure of central tendency that works for categorical data like favourite colour, sport, or fruit.
Q6. How do you find the mode from a frequency table?
Look at the frequency column. The value with the largest frequency is the mode.
Q7. Why is mode useful in real life?
Mode helps businesses decide what to stock more of (most popular size), helps schools identify common scores, and helps weather forecasters identify typical conditions.
Q8. Does arranging data in order help?
Yes. Arranging in order groups identical values together, making it easier to spot the most frequent value.
Q9. Is mode taught in the NCERT Class 5 syllabus?
Yes. Mode is part of the Data Handling chapter in NCERT/CBSE Class 5 Maths, along with mean and basic data representation.
