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What is Median?
Grade Level:
Class 12
AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics
Definition
What is it?
The Median is the middle value in a list of numbers that has been arranged in order from smallest to largest. It helps us find the 'center' of a dataset without being affected too much by very large or very small numbers.
Simple Example
Quick Example
Imagine your family's daily chai expenses for a week: ₹10, ₹15, ₹12, ₹100 (special guest!), ₹18, ₹15, ₹12. To find the median expense, first arrange them in order: ₹10, ₹12, ₹12, ₹15, ₹15, ₹18, ₹100. The middle value is ₹15.
Worked Example
Step-by-Step
Let's find the median marks of 5 students in a Math test: 45, 78, 62, 91, 55.
1. Arrange the marks in ascending order (smallest to largest): 45, 55, 62, 78, 91.
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2. Count the total number of values (n). Here, n = 5.
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3. Since n is an odd number, the median is the value at the position (n+1)/2.
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4. Calculate the position: (5+1)/2 = 6/2 = 3rd position.
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5. Look at the ordered list and find the value at the 3rd position.
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6. The value at the 3rd position is 62.
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Answer: The median mark is 62.
Why It Matters
Understanding the median is crucial in many fields! In FinTech, it helps analyze typical income without extreme outliers skewing results. Doctors use it in medicine to understand typical patient responses. Even AI/ML engineers use median to process data and make better predictions.
Common Mistakes
MISTAKE: Not arranging the numbers in order before finding the middle value. | CORRECTION: Always arrange the data (ascending or descending) first. This is the most important step!
MISTAKE: Confusing median with mean (average). | CORRECTION: Mean is the sum of all values divided by the count. Median is the middle value after ordering. They are different 'centers' of data.
MISTAKE: For an even number of data points, picking only one of the two middle numbers. | CORRECTION: When 'n' is even, take the average (mean) of the two middle values.
Practice Questions
Try It Yourself
QUESTION: Find the median of these daily temperatures in degrees Celsius: 28, 32, 25, 30, 29. | ANSWER: 29
QUESTION: A mobile shop sold these numbers of phones over 6 days: 15, 22, 18, 20, 17, 25. What is the median number of phones sold? | ANSWER: 19
QUESTION: The run scores of a cricketer in 7 matches are: 40, 10, 85, 0, 55, 120, 25. Find the median score. If he scores 60 in his next match, what will be the new median score? | ANSWER: Original Median: 40. New Median: 55
MCQ
Quick Quiz
What is the first step to find the median of a given set of numbers?
Add all the numbers together
Count the total number of values
Arrange the numbers in ascending or descending order
Divide the largest number by the smallest number
The Correct Answer Is:
C
The correct answer is C. Arranging the numbers in order is the essential first step to correctly identify the middle value. Without ordering, you cannot find the true median.
Real World Connection
In the Real World
When you see news reports about the 'median salary' in India or the 'median age' of a population, they are using this exact concept. For instance, Swiggy or Zomato might use median delivery times to understand typical service speed, as a single very long delivery wouldn't skew the 'average' as much as it would the mean.
Key Vocabulary
Key Terms
DATASET: A collection of related information or numbers | ASCENDING ORDER: Arranging numbers from smallest to largest | DESCENDING ORDER: Arranging numbers from largest to smallest | OUTLIER: A data point that is much larger or much smaller than most other data points | CENTRAL TENDENCY: A single value that attempts to describe a set of data by identifying the central position within that set of data (mean, median, mode are measures of central tendency).
What's Next
What to Learn Next
Great job understanding the median! Next, explore 'Mode' and 'Mean' to learn about other ways to find the 'center' of data. Comparing all three will give you a complete picture of how to analyze any dataset!
