Understanding Mean, Median, and Mode is fundamental in data interpretation and statistical analysis. These concepts not only play a significant role in our daily lives—such as analysing expenses or test scores—but are also essential components in competitive government exams like SSC, RRB, and other aptitude-based tests. Mastering these topics enhances your analytical thinking and problem-solving skills.
Mean
Definition: The mean is the average of a set of values, calculated by dividing the sum of all values by the number of values.
Formula:
- Types of Mean:
- Arithmetic Mean – E.g., (5 + 10 + 15)/3 = 10
- Weighted Mean – When different values have different levels of importance.
Real-life example: Calculating average marks in subjects.
Example of Weighted Mean
A shopper buys: 2 kg of rice at ₹50 per kg, 1.5 kg of dal at ₹80 per kg and 3 kg of sugar at ₹40 per kg
What is the average price per kg of the total purchase?
- Answer :
- Weights (quantities): 2 kg, 1.5 kg, 3 kg
- Prices per kg (values): ₹50, ₹80, ₹40
Weighted Mean = (w₁x₁ + w₂x₂ + w₃x₃) / (w₁ + w₂ + w₃)
= (2×50 + 1.5×80 + 3×40) / (2 + 1.5 + 3)
= (100 + 120 + 120) / 6.5
= 340 / 6.5
= ₹52.31
Median
Definition: The median is the middle value when data is arranged in order.
Formula:
- If number of values (n) is odd: Median = value at position (n+1)/2
- If n is even: Median = average of values at positions n/2 and (n/2)+1
Real-life example: Finding the middle salary in a company to study income distribution.
Mode
Definition: Mode is the value that appears most frequently in a dataset.
Types of Mode:
- Unimodal: One mode
- Bimodal: Two modes
- Multimodal: More than two modes
Real-life example: Identifying the most sold shoe size in a shop.
1. What is the arithmetic mean of 6, 8, 10, 12, and 14?
A) 8 B) 9 C) 10 D) 11
2. What is the median of the set: 4, 7, 1, 9, 3?
A) 3 B) 4 C) 5 D) 7
3. Find the mode of 2, 4, 4, 6, 8.
A) 2 B) 4 C) 6 D) 8
4. Which measure of central tendency is most affected by extreme values?
A) Mean B) Median C) Mode D) None
5. The median of 10, 12, 14, 16, 18, 20 is:
A) 15 B) 16 C) 17 D) 14
6. If the mode of a dataset is 25, which of the following is true?
A) 25 occurs most often B) 25 is the highest value C) 25 is the average D) None
Mean, Median, and Mode are essential tools in statistical analysis. They are not just mathematical concepts but real-world decision-making aids. In exams, knowing when and how to apply each can make a significant difference. Practice regularly and build confidence for exam success.
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