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What is a Cumulative Frequency Distribution?
Grade Level:
Class 12
AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics
Definition
What is it?
A Cumulative Frequency Distribution shows the total frequency of all values up to a certain point in a dataset. It tells us how many observations are less than or equal to a particular value, by adding up frequencies step-by-step.
Simple Example
Quick Example
Imagine your class has 20 students. If 5 students scored less than 60 marks and 8 students scored less than 70 marks, then the cumulative frequency for 'less than 70 marks' would be 8. It's like counting how many people have finished a certain number of laps in a race.
Worked Example
Step-by-Step
Let's say a chaiwala sold cups of chai over 5 days: Day 1: 20 cups, Day 2: 25 cups, Day 3: 30 cups, Day 4: 28 cups, Day 5: 35 cups. Let's find the cumulative frequency of cups sold.
Step 1: For Day 1, cumulative frequency is just the frequency for Day 1. So, 20 cups.
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Step 2: For Day 2, add Day 2's frequency to Day 1's cumulative frequency. So, 20 + 25 = 45 cups.
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Step 3: For Day 3, add Day 3's frequency to Day 2's cumulative frequency. So, 45 + 30 = 75 cups.
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Step 4: For Day 4, add Day 4's frequency to Day 3's cumulative frequency. So, 75 + 28 = 103 cups.
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Step 5: For Day 5, add Day 5's frequency to Day 4's cumulative frequency. So, 103 + 35 = 138 cups.
Answer: The cumulative frequencies are 20, 45, 75, 103, and 138 cups respectively.
Why It Matters
Understanding cumulative frequency helps in fields like AI/ML to analyze data patterns, in FinTech to understand market trends, and in Climate Science to track changes over time. Data scientists and economists use it to make important predictions and decisions.
Common Mistakes
MISTAKE: Forgetting to add the previous cumulative frequency and only adding the current frequency. | CORRECTION: Always add the current frequency to the cumulative frequency of the previous class interval.
MISTAKE: Calculating cumulative frequency from bottom to top (decreasing order) instead of top to bottom (increasing order). | CORRECTION: Cumulative frequency is always calculated by adding frequencies from the first class interval downwards.
MISTAKE: Confusing cumulative frequency with simple frequency. | CORRECTION: Simple frequency tells you how many times an event occurs in a specific interval, while cumulative frequency tells you the total count up to that interval.
Practice Questions
Try It Yourself
QUESTION: A class has students with the following scores in a Math test: 10, 15, 20, 25, 30. If 2 students scored 10, 3 scored 15, 5 scored 20, 4 scored 25, and 1 scored 30. What is the cumulative frequency for students scoring up to 20 marks? | ANSWER: 10 students
QUESTION: The number of auto-rickshaws passing a signal in one-hour intervals are: 8, 12, 10, 15, 7. Calculate the cumulative frequency for each interval. | ANSWER: 8, 20, 30, 45, 52
QUESTION: A mobile data company recorded daily data usage (in GB) for a week: Monday: 50, Tuesday: 60, Wednesday: 45, Thursday: 70, Friday: 55, Saturday: 80, Sunday: 65. What is the cumulative data usage at the end of Friday? | ANSWER: 280 GB
MCQ
Quick Quiz
What does the last value in a cumulative frequency distribution represent?
The frequency of the last class interval
The total number of observations in the dataset
The average frequency of all class intervals
The median value of the dataset
The Correct Answer Is:
B
The last value in a cumulative frequency distribution is the sum of all individual frequencies, which equals the total number of observations in the dataset. It represents the total count up to the very end.
Real World Connection
In the Real World
In cricket, commentators use cumulative frequencies when they talk about 'total runs scored by a team up to the 10th over' or 'how many deliveries a bowler has bowled in total'. This helps them analyze game progress and predict outcomes, similar to how data analysts track product sales on e-commerce sites like Flipkart or Amazon.
Key Vocabulary
Key Terms
FREQUENCY: The number of times a particular event or value occurs | CUMULATIVE: Increasing or growing by successive additions | DATASET: A collection of related data | CLASS INTERVAL: A range of values used to group data in a frequency distribution
What's Next
What to Learn Next
Now that you understand cumulative frequency, you're ready to learn about 'Ogive' or 'Cumulative Frequency Curve'. This visual representation uses cumulative frequencies to help us quickly estimate values like the median, which is super useful for quick data analysis!
