Class 7 - Mode: Concept, Steps, and Solved Examples

'Mode' is a fundamental concept in Class 7 mathematics that refers to the value that occurs most frequently in a given dataset. It is one of the key measures of central tendency, alongside mean and median. The mode helps in quickly determining the most popular or common outcome. In this guide, you will learn the definition of mode and the method to calculate it and explore solved examples to develop a clear and easy understanding of the concept.

Table of Contents

• What Is Mode?
• How to Find the Mode
• Types of Mode
• Properties of Mode
• Solved Examples on Mode
• Mean vs Median vs Mode
• Practice Questions on Mode

What Is Mode?

The observation which occurs for a maximum number of times is called the

mode of the given data. The mode is the value that occurs most frequently in a dataset.

Note:

• Data can have one mode, multiple modes, or no mode.

• There is no mode when all values occur only once.

For example, in the dataset 3, 7, 5, 7, 2, 9, 7, 4, the number 7 appears three times, more than any other value. So the mode of the data set is 7.

How to Find the Mode

Mode formula: The mode of ungrouped data has no complex formula. It is simply:

Mode = the observation with the highest frequency

To find the mode of a dataset, follow the steps below:

Step 1: List out all the values in the dataset.

Step 2: Count how many times each value appears.

Step 3: The value with the highest frequency is the mode.
If two or more values tie for highest frequency, both (or all) are modes.

If no value repeats, the dataset has no mode.

Types of Mode

A dataset can have more than one mode or no mode at all. This leads to four distinct types.

1. Unimodal: A dataset with exactly one mode.

One value stands out as the most frequent.

Example: {3, 7, 7, 9, 11, 13, 7, 5}

Mode = 7 (appears 3 times; all others appear once)

2. Bimodal: A dataset with exactly two modes.

Both values appear the same number of times, and that frequency is higher than all other values.

Example: {4, 9, 9, 13, 16, 16, 21, 25}

Frequency count: 9 occurs 2 times; 16 occurs 2 times; all occurs appear 1 time only

Mode = 9 and 16

3. Trimodal: A dataset with exactly three modes.

Example: {2, 2, 2, 5, 7, 7, 7, 10, 15, 15, 15, 18}

Frequency count: 2 occurs 3 times; 7 occurs 3 times; 15 occurs 3 times; others occurs 1 time only

Mode = 2, 7, and 15

4. Multimodal: A dataset with four or more modes.

Example: {10, 10, 14, 14, 18, 18, 22, 22, 30}

Frequency count: 10, 14, 18, and 22 occur 2 times, and 30 occurs only 1 time.

Mode = 10, 14, 18, and 22

When a dataset is multimodal, the mode loses its descriptive power, and it's hard to say anything meaningful when four values are equally the "most common".

Properties of Mode

• Mode is the only measure of central tendency that can be used for qualitative (non-numerical) data.

• Mode is not affected by extreme values

• A dataset may have no mode, one mode, or multiple modes.

Solved Examples on Mode

Example 1: Find the mode of 14, 21, 14, 28, 14, 35, 42, 21.
Solution: The number 14 occurs 3 times and 21 occurs 2 times, while 28, 35, and 42 each occur once.
Therefore, the mode is 14, as it has the highest frequency.

Example 2: Find the mode of 7, 13, 19, 25, 31, 37.
Solution: Since each value appears exactly once. No mode exists for this dataset.

Example 3: Given below are the marks scored by Uday in a test in 6 subjects:25, 20, 20, 22, 21, 19. Find the mode of the marks scored.
Solution: Arrange the given data in ascending order. 19, 20, 20, 21, 22, 25. The value 20 occurs the most. ⸫ Mode = 20.

Example 4: The marks obtained out of 50 by 35 students in a test are given in the frequency table that follows:

Find the mode.
Solution: The students who got 39 marks are more compared to others from the table above.
⸫ Mode = 39

Example 5: The ages (in years) of the racers in a bicycle race are 22, 18, 19, 21, 25, 25, 21, 20, 17, 21, 23, and 26. Find the mode of the given data.
Solution: Arranging the data in ascending order gives 17, 18, 19, 20, 21, 21, 21, 22, 23, 25, 25, 26
21 appears 3 times, 25 appears 2 times, and all other values appear once. The value with the highest frequency is 21.
Therefore, the mode of the given data is 21 years.

Mean vs Median vs Mode

Mean, median, and mode are measures of central tendency used to represent a dataset with a single value. While the mean gives the average, the median shows the middle value, and the mode identifies the most frequently occurring number.

Practice Questions on Mode

1. Find the mode of the given data: 20, 14, 18, 9, 11, 9, 5, 14, 13

2. Find the mode of the given data: 12, 14, 17, 19, 18, 19, 17, 14, 15, 11, 19, 18, 17, 18, 15, 12, 15, 13, 19.

3. Adlin was playing a game of dice. The values that Adlin threw 20 times are listed below: 3, 4, 6, 2, 3, 5, 1, 3, 5, 4, 1, 3, 5, 1, 5, 3, 2, 3, 3, 6. Determine the mode.

4. The marks obtained by 8 students in a test are 23, 24, 26, 30, 26, 27, 26 and 25. Find the mode of the students’ marks.

5. The runs scored in a cricket match by 11 players is as follows: 7, 18, 121, 51, 105, 71, 1, 16, 9, 11, 15. Find the mode from the given data.