How to Find Mode in Statistics (Step-by-Step Guide)
The concept of mode in maths plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios.
What Is Mode in Maths?
The mode in maths is defined as the value that appears most frequently in a data set. In other words, it’s the number (or numbers) seen the highest number of times among all observations. You’ll find this concept applied in areas such as statistics, science research, and real-world data like most popular items or survey responses.
Key Formula for Mode in Maths
For ungrouped data, simply identify the number with the highest frequency.
For grouped (continuous) data:
Here’s the standard formula: \( \text{Mode} = l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h \)
| Symbol | Meaning |
|---|---|
| l | Lower limit of modal class |
| f1 | Frequency of modal class |
| f0 | Frequency of class before modal class |
| f2 | Frequency of class after modal class |
| h | Class interval width |
Cross-Disciplinary Usage
Mode in maths is not only useful in statistics, but also plays an important role in Biology (finding the most common trait in a population), Computer Science (most frequent data value), and even in economics (most bought product). Students preparing for board exams, JEE, NEET, or Olympiads will see its relevance in several questions. Vedantu teaches how to calculate mode in simple ways for all subjects.
Step-by-Step Illustration
Find the mode of the following data set: 4, 7, 9, 7, 6, 7, 9, 4, 6, 7
1. Count how many times each number appears:4 appears 2 times
6 appears 2 times
7 appears 4 times
9 appears 2 times
2. The number 7 appears most frequently.
3. Final Answer: Mode = 7
Example for Grouped Data:
1. Find the modal class (class with highest frequency)2. Use the grouped data mode formula:
Suppose l = 10, f1 = 7, f0 = 3, f2 = 2, h = 5
3. Plug in the values:
Mode = 10 + ((7–3) ÷ (2×7–3–2)) × 5
= 10 + (4 ÷ 9) × 5
= 10 + (0.444…) × 5
= 10 + 2.22
Final Answer: Mode ≈ 12.22
Speed Trick or Practical Shortcut
When working with a small data set, sort the data and spot repeats. For large lists or exam MCQs, use a tally table or a frequency table to see which value occurs the most. In grouped data, the class interval with the highest frequency is always the modal class—no need to check all others!
Example Trick: If a number appears more than once, and no other number appears as often, it's the mode. If two or more numbers have the highest and equal frequency, the data set is bimodal/multimodal.
Try These Yourself
- Find the mode of: 3, 5, 6, 8, 6, 8, 8, 3, 5, 8.
- Identify if this set has a mode: 11, 12, 13, 14, 15.
- For the frequencies below, find the modal value:
Class Intervals: 0-10, 10-20, 20-30
Frequencies: 2, 7, 3 - Is it possible for a data set to have no mode? Explain.
Frequent Errors and Misunderstandings
- Assuming mode is always unique (it can be bimodal or multimodal).
- Confusing “mode” with “mean” (average) or “median” (middle value).
- Not arranging grouped data before applying the mode formula.
- Missing out on mode in non-numerical/categorical data (e.g. most popular color).
Relation to Other Concepts
The idea of mode in maths connects closely with mean, median, and other measures of central tendency like median and mean. Mastering mode helps in understanding statistics, data analysis, and probability.
Types of Mode
| Type | Meaning | Example |
|---|---|---|
| Unimodal | One mode | 2, 3, 3, 5 (mode = 3) |
| Bimodal | Two modes | 4, 5, 5, 7, 7 (modes = 5 and 7) |
| Multimodal | More than two modes | 1, 2, 2, 3, 3, 4, 4 (modes = 2, 3, 4) |
| No mode | No repeated value | 1, 2, 3, 4, 5 |
Mode vs. Mean & Median
| Measure | How Found | Sensitive to Outliers? |
|---|---|---|
| Mode | Most frequent value | No |
| Mean | Sum ÷ Count | Yes |
| Median | Middle value | No |
Classroom Tip
A quick way to remember mode: “Mode is Most Often.” Just look for the number that pops up most! Vedantu’s teachers use color tricks (highlighting repeats) to help students spot the mode fast in live classes.
We explored mode in maths—from definition, formula, examples, mistakes, and connections to other subjects. Continue practicing with Vedantu to become confident in solving problems using this concept.
FAQs on What is Mode in Maths?
1. What is the mode in math?
In mathematics, the mode is the value that appears most frequently in a data set. It is a measure of central tendency used to identify the most common or repeated number among a group of numbers. Unlike the mean and median, the mode can be used for both numerical and categorical data. For example, in the set {2, 2, 3, 5, 7}, the mode is 2 as it occurs more times than any other number.
2. What is the mode of 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10?
To determine the mode of the data set {10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10}, count the frequency of each number:
- 10 appears 3 times
- 11 appears 2 times
- Rest appear once
3. What is example mode?
An example of mode is found by looking at a set of numbers and finding which value repeats the most. For instance, in the data set {4, 6, 8, 6, 7, 6, 9}, the number 6 appears three times, making it the mode. The mode helps in identifying the most popular or frequent item in a collection.
4. What is the mode of 10 8 4 7 11 15 8 6 and 8?
In the data set {10, 8, 4, 7, 11, 15, 8, 6, 8}, you need to determine which number occurs the most.
- 8 appears 3 times
- All others appear only once
5. How is the mode calculated in a data set?
To calculate the mode in a data set, follow these steps:
- List all numbers in the data set.
- Count how many times each number appears.
- The number with the highest frequency is the mode.
6. What happens if there is no mode in the data?
If no number in a data set repeats, all numbers occur with the same frequency, and there is no mode. For example, in the set {3, 5, 7, 9}, each value appears only once. In such cases, the data is said to have no mode.
7. Can a data set have more than one mode?
Yes, a data set can have more than one mode. When two values repeat with equal and highest frequency, the set is bimodal. If more than two values occur most frequently, the set is called multimodal. For example, in {2, 3, 3, 5, 5, 7}, both 3 and 5 are modes.
8. How is mode different from mean and median?
Mode is the value that appears most frequently in a data set.
Mean is the average of all values, calculated as $\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$.
Median is the middle value when the values are arranged in order.
All three are measures of central tendency but highlight different aspects of the data.
9. What is the importance of mode in real-life situations?
The mode is essential in real life for understanding patterns where the most frequent observation is important. For example:
- Identifying the most sold size of a uniform in a school
- Determining the most popular answer in surveys
- Analyzing customer preferences in business data
10. How can students practice finding the mode using Vedantu’s resources?
Students can practice finding the mode by exploring Vedantu’s variety of study materials, interactive worksheets, and live online classes. Vedantu offers engaging exercises and expert guidance that help students understand how to calculate and interpret mode, along with other statistics concepts, effectively.
