What is 'More Than' Cumulative Frequency? | Simple Explanation for Class 12

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What is a 'More Than' Cumulative Frequency?

Grade Level:

Class 12

AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics

Definition

What is it?

A 'More Than' Cumulative Frequency tells you how many data points are *greater than or equal to* a certain value. Instead of adding frequencies upwards, you add them downwards, starting from the highest value and going lower. It helps us see how many observations are above a particular threshold.

Simple Example

Quick Example

Imagine your school has 50 students. If a 'More Than' cumulative frequency table shows that 35 students scored 'more than or equal to 60 marks' in an exam, it means 35 students got 60 marks or higher. This helps the teacher quickly see how many students performed above a certain level.

Worked Example

Step-by-Step

Let's say we have marks of 20 students in a test:
Marks: 0-20 (3 students), 20-40 (5 students), 40-60 (7 students), 60-80 (4 students), 80-100 (1 student).

Step 1: Identify the lower limits of the class intervals. These are 0, 20, 40, 60, 80.
---Step 2: Start with the total number of students. Here, it's 3 + 5 + 7 + 4 + 1 = 20 students.
---Step 3: For 'More than or equal to 0 marks', the cumulative frequency is the total number of students, which is 20.
---Step 4: For 'More than or equal to 20 marks', subtract the frequency of the 0-20 class (3 students) from the previous cumulative frequency (20). So, 20 - 3 = 17.
---Step 5: For 'More than or equal to 40 marks', subtract the frequency of the 20-40 class (5 students) from the previous cumulative frequency (17). So, 17 - 5 = 12.
---Step 6: For 'More than or equal to 60 marks', subtract the frequency of the 40-60 class (7 students) from the previous cumulative frequency (12). So, 12 - 7 = 5.
---Step 7: For 'More than or equal to 80 marks', subtract the frequency of the 60-80 class (4 students) from the previous cumulative frequency (5). So, 5 - 4 = 1.

Answer: The 'More Than' Cumulative Frequencies are: More than or equal to 0: 20, More than or equal to 20: 17, More than or equal to 40: 12, More than or equal to 60: 5, More than or equal to 80: 1.

Why It Matters

Understanding 'More Than' cumulative frequency is crucial in fields like AI/ML for analyzing data trends and in FinTech for assessing risk by looking at how many investments are above a certain value. Engineers use it to see how many components exceed a minimum quality standard, helping them make better products.

Common Mistakes

MISTAKE: Adding frequencies upwards like a 'Less Than' cumulative frequency | CORRECTION: Remember 'More Than' means you subtract frequencies from the total as you move down the class intervals.

MISTAKE: Using the upper limit of the class interval for 'More Than' | CORRECTION: Always use the *lower limit* of the class interval when calculating 'More Than' cumulative frequency, as it represents 'greater than or equal to' that value.

MISTAKE: Forgetting to start with the total frequency for the first 'More Than' class | CORRECTION: The cumulative frequency for the lowest class interval (e.g., 'more than or equal to 0') is always the *total* frequency of all observations.

Practice Questions

Try It Yourself

QUESTION: A vegetable vendor sells potatoes. The number of customers buying different weights are: 0-1 kg (10 customers), 1-2 kg (15 customers), 2-3 kg (8 customers), 3-4 kg (5 customers). What is the 'More Than' cumulative frequency for 'More than or equal to 2 kg'? | ANSWER: Total customers = 10+15+8+5 = 38. For 'More than or equal to 0 kg' = 38. For 'More than or equal to 1 kg' = 38 - 10 = 28. For 'More than or equal to 2 kg' = 28 - 15 = 13. So, 13 customers.

QUESTION: The daily earnings (in Rupees) of 40 auto-rickshaw drivers are: 0-200 (2 drivers), 200-400 (10 drivers), 400-600 (15 drivers), 600-800 (8 drivers), 800-1000 (5 drivers). Find the 'More Than' cumulative frequency for 'More than or equal to 600 Rupees'. | ANSWER: Total drivers = 40. More than or equal to 0 = 40. More than or equal to 200 = 40 - 2 = 38. More than or equal to 400 = 38 - 10 = 28. More than or equal to 600 = 28 - 15 = 13. So, 13 drivers.

QUESTION: In a survey of mobile data usage (in GB) per month by 100 students: 0-5 GB (20 students), 5-10 GB (35 students), 10-15 GB (30 students), 15-20 GB (15 students). Create a complete 'More Than' cumulative frequency table. | ANSWER: More than or equal to 0 GB: 100, More than or equal to 5 GB: 100 - 20 = 80, More than or equal to 10 GB: 80 - 35 = 45, More than or equal to 15 GB: 45 - 30 = 15.

MCQ

Quick Quiz

If a 'More Than' cumulative frequency for 'More than or equal to 50 runs' in a cricket match is 25, what does this mean?

25 players scored exactly 50 runs.

25 players scored less than 50 runs.

25 players scored 50 runs or more.

25 players scored more than 50 runs but less than 100 runs.

The Correct Answer Is:

A 'More Than' cumulative frequency tells us the number of observations greater than or equal to a specific value. So, 25 players scored 50 runs or more.

Real World Connection

In the Real World

Imagine a company like Zomato or Swiggy analyzing delivery times. They might use 'More Than' cumulative frequency to see how many deliveries take 'more than or equal to 30 minutes'. This helps them understand service quality and identify areas for improvement to keep customers happy.

Key Vocabulary

Key Terms

FREQUENCY: The number of times a particular value or item appears in a dataset. | CUMULATIVE FREQUENCY: The running total of frequencies. | CLASS INTERVAL: A range of values used to group data. | LOWER LIMIT: The smallest value in a class interval. | UPPER LIMIT: The largest value in a class interval.

What's Next

What to Learn Next

Now that you understand 'More Than' cumulative frequency, you should explore how to draw a 'More Than' Ogive. This graph visually represents this data and helps you estimate values like the median directly from the curve, which is super useful!