Mode of Data
Suppose a shoe shop owner wants to know which shoe size to stock the most. He checks the sizes sold last week: 6, 7, 7, 8, 7, 9, 7, 8, 6, 7. The size that was sold the most is size 7. In mathematics, the value that appears most often in a data set is called the mode.
The mode is one of the three measures of central tendency, along with the mean and median. It tells you which value is the most common or popular.
In Class 7 NCERT Maths, you will learn how to find the mode of different data sets, including cases where there is no mode or more than one mode.
What is Mode of Data - Grade 7 Maths (Data Handling)?
Definition: The mode of a data set is the observation that occurs the most number of times (has the highest frequency).
- A data set can have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal).
- If no value is repeated, the data set has no mode.
Mode of Data Formula
How to find the mode:
Mode = Observation with the highest frequency
Steps:
- List all the observations.
- Count how many times each observation appears (its frequency).
- The observation with the highest frequency is the mode.
Types and Properties
Types based on the number of modes:
- Unimodal: Data has exactly one mode. Example: 2, 3, 3, 4, 5. Mode = 3.
- Bimodal: Data has exactly two modes. Example: 1, 2, 2, 3, 4, 4, 5. Modes = 2 and 4.
- Multimodal: Data has more than two modes. Example: 1, 1, 2, 2, 3, 3. Modes = 1, 2, and 3.
- No mode: No value is repeated. Example: 5, 8, 12, 15, 20. There is no mode.
Solved Examples
Example 1: Finding the Mode (Simple Data)
Problem: Find the mode of: 4, 7, 3, 7, 2, 7, 5, 3.
Solution:
Step 1: Count frequencies:
- 2 appears 1 time
- 3 appears 2 times
- 4 appears 1 time
- 5 appears 1 time
- 7 appears 3 times
Step 2: The highest frequency is 3 (for the value 7).
Answer: The mode is 7.
Example 2: Bimodal Data
Problem: Find the mode of: 10, 20, 20, 30, 30, 40.
Solution:
Step 1: Count frequencies:
- 10 appears 1 time
- 20 appears 2 times
- 30 appears 2 times
- 40 appears 1 time
Step 2: Both 20 and 30 have the highest frequency (2 each).
Answer: The data is bimodal with modes 20 and 30.
Example 3: No Mode
Problem: Find the mode of: 5, 10, 15, 20, 25.
Solution:
Each value appears exactly once. No value is repeated.
Answer: This data set has no mode.
Example 4: Mode of Favourite Colours
Problem: 15 students were asked their favourite colour. The responses were: Red, Blue, Green, Blue, Red, Blue, Yellow, Blue, Green, Red, Blue, Yellow, Red, Green, Blue.
Find the mode.
Solution:
Step 1: Count frequencies:
- Red: 4
- Blue: 6
- Green: 3
- Yellow: 2
Step 2: Blue has the highest frequency (6).
Answer: The mode is Blue.
Example 5: Mode from a Frequency Table
Problem: The marks obtained by students are shown below:
- Marks: 5, 6, 7, 8, 9
- Number of students: 3, 7, 5, 4, 1
Find the mode.
Solution:
The highest frequency is 7, which corresponds to marks = 6.
Answer: The mode is 6 marks.
Example 6: Mode of Shoe Sizes
Problem: Shoe sizes sold in a day: 5, 6, 7, 7, 8, 7, 6, 9, 7, 8, 7. Find the mode.
Solution:
- 5: 1 time
- 6: 2 times
- 7: 5 times
- 8: 2 times
- 9: 1 time
Answer: The mode is 7 (sold most frequently).
Example 7: Mean, Median and Mode Together
Problem: Find the mean, median, and mode of: 2, 3, 4, 4, 5.
Solution:
Mean: (2 + 3 + 4 + 4 + 5) / 5 = 18 / 5 = 3.6
Median: Data in order: 2, 3, 4, 4, 5. Middle (3rd) value = 4
Mode: 4 appears twice (most frequent). Mode = 4
Answer: Mean = 3.6, Median = 4, Mode = 4.
Example 8: Mode of Dice Rolls
Problem: A dice is rolled 12 times. The outcomes are: 3, 5, 2, 3, 6, 1, 3, 4, 2, 5, 3, 1. Find the mode.
Solution:
- 1: 2 times
- 2: 2 times
- 3: 4 times
- 4: 1 time
- 5: 2 times
- 6: 1 time
Answer: The mode is 3 (appeared most often).
Real-World Applications
Real-life uses of the mode:
- Retail: Shop owners use the mode to find the most popular product size, colour, or brand to stock more of it.
- Fashion: Clothing manufacturers check which sizes are ordered most (the mode) and produce more of those sizes.
- Transport: Traffic planners find the mode of peak traffic times to plan signals and road expansions.
- Elections: The candidate who gets the most votes (the mode of votes) wins the election.
- Food industry: Restaurants find the most ordered dish (mode) and ensure they have enough ingredients for it.
Key Points to Remember
- The mode is the observation with the highest frequency.
- A data set can have no mode, one mode, two modes (bimodal), or more.
- The mode is the only measure of central tendency that can be used with non-numerical data (like colours, names).
- The mode is not affected by extreme values.
- If all values occur equally often, there is no mode.
- Mode is useful when you want to find the most common or popular item.
- Mode, mean, and median can all be different for the same data set.
Practice Problems
- Find the mode of: 8, 5, 3, 8, 9, 5, 8, 2.
- Find the mode of: 12, 15, 18, 12, 18, 20. Is this unimodal or bimodal?
- Find the mode of: 1, 2, 3, 4, 5, 6.
- The favourite fruits of 10 students are: Apple, Mango, Banana, Mango, Apple, Mango, Grapes, Apple, Mango, Banana. Find the mode.
- A class test has the following scores: 6(3 students), 7(5 students), 8(4 students), 9(2 students), 10(1 student). Find the mode.
- Find the mean, median and mode of: 5, 7, 7, 8, 10.
Frequently Asked Questions
Q1. What is the mode of a data set?
The mode is the value that appears most often in a data set. For example, in 2, 3, 3, 4, 5, the mode is 3 because it appears twice while all other values appear once.
Q2. Can a data set have more than one mode?
Yes. If two values tie for the highest frequency, the data is bimodal (two modes). If more than two values tie, it is multimodal. For example, in 1, 1, 2, 2, 3, both 1 and 2 are modes.
Q3. What if no value is repeated?
If every value appears exactly once, the data set has no mode. For example, 5, 10, 15, 20 has no mode.
Q4. Can the mode be used for non-numerical data?
Yes. The mode is the only measure of central tendency that works for non-numerical (categorical) data like colours, names, or brands. For example, if the most common eye colour in a class is brown, then brown is the mode.
Q5. Is the mode always equal to the mean or median?
No. The mean, median, and mode can all be different. For example, in the data 1, 2, 2, 3, 7: mean = 3, median = 2, mode = 2. They happen to match sometimes but not always.
Q6. When is the mode the best measure to use?
The mode is best when you want to find the most common or popular item, especially with non-numerical data. For example, finding the most popular pizza topping or the most common shoe size.
