What is Mode from a Frequency Distribution?

S3-SA3-0302

Grade Level:

Class 8

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Mode from a Frequency Distribution is the value or item that appears most often in a dataset. When data is organised into a frequency distribution table, the mode is simply the value that has the highest frequency.

Simple Example

Quick Example

Imagine a class of students took a math test, and their scores out of 10 were: 7, 8, 5, 7, 9, 7, 6. If we count how many times each score appears, 7 appears 3 times, which is more than any other score. So, the mode score is 7.

Worked Example

Step-by-Step

Let's find the mode for the number of siblings students have:

Number of Siblings (x): 0, 1, 2, 3, 4
Frequency (f): 5, 12, 8, 3, 1

---1. Understand the table: The first row 'Number of Siblings (x)' tells us the different values (0, 1, 2, 3, 4 siblings). The second row 'Frequency (f)' tells us how many students have that many siblings (e.g., 5 students have 0 siblings, 12 students have 1 sibling).

---2. Look for the highest frequency: Scan the 'Frequency (f)' row to find the largest number. In this case, the frequencies are 5, 12, 8, 3, 1. The largest frequency is 12.

---3. Identify the corresponding value: See which 'Number of Siblings (x)' value corresponds to this highest frequency. The frequency 12 corresponds to '1' sibling.

---4. State the mode: The value with the highest frequency is the mode.

Answer: The Mode is 1.

Why It Matters

Understanding mode helps in fields like AI/ML to identify common patterns in data, or in economics to find the most popular product. Data scientists and market researchers use mode to understand customer preferences and make informed decisions.

Common Mistakes

MISTAKE: Stating the highest frequency as the mode. | CORRECTION: The mode is the DATA VALUE (x) that has the highest frequency, not the frequency itself.

MISTAKE: Confusing mode with mean or median. | CORRECTION: Mode is about the most frequent item, while mean is the average, and median is the middle value. They are all different ways to describe data.

MISTAKE: Thinking there can only be one mode. | CORRECTION: A dataset can have one mode (unimodal), two modes (bimodal), or even more (multimodal) if two or more values have the same highest frequency.

Practice Questions

Try It Yourself

QUESTION: Find the mode for the following data:
Favourite Colour (x): Red, Blue, Green, Yellow
Number of Students (f): 7, 10, 5, 7
| ANSWER: Blue

QUESTION: In a survey, the number of mobile phones owned by families was recorded:
Number of Phones (x): 1, 2, 3, 4, 5
Number of Families (f): 8, 15, 12, 6, 2
What is the mode?
| ANSWER: 2

QUESTION: A shopkeeper recorded the number of shirts sold in different sizes:
Shirt Size (x): S, M, L, XL, XXL
Number of Shirts Sold (f): 25, 40, 40, 30, 15
What is the mode(s) of shirt sizes?
| ANSWER: M and L (This is a bimodal distribution)

MCQ

Quick Quiz

For the data given below, what is the mode?
Daily Chai Sold (litres): 20, 25, 30, 35, 40
Number of Days (f): 3, 7, 9, 5, 2

3 litres

9 days

30 litres

25 litres

The Correct Answer Is:

The highest frequency is 9, which corresponds to selling 30 litres of chai. So, the mode is 30 litres. Options A and B are incorrect because they are either a frequency or an incorrect data value.

Real World Connection

In the Real World

Think about online shopping platforms like Flipkart or Amazon. They often show 'most popular' or 'frequently bought together' items. This is a real-world application of mode, helping them recommend products based on what most people are buying. Even food delivery apps like Zomato or Swiggy might use mode to show which dishes are ordered most often in your area.

Key Vocabulary

Key Terms

FREQUENCY: How many times a particular value appears in a dataset | DATASET: A collection of related information or numbers | DISTRIBUTION: How data is spread out or organised | UNIMODAL: A dataset with one mode | BIMODAL: A dataset with two modes

What's Next

What to Learn Next

Great job understanding mode! Next, you should learn about Mean and Median from a frequency distribution. These are other important ways to find the 'average' or 'centre' of a dataset, and knowing all three will give you a complete picture of your data.