Mean, Median & Mode – Solved Problems with Explanation
Mean, Median, and Mode are measures of central tendency. They help us understand the typical or central value of a data set and are widely used in statistics, economics, and everyday data analysis.
In this article, we solve multiple problems on Mean, Median, and Mode with clear step-by-step explanations suitable for school exams and competitive tests.
Basic Definitions
- Mean: Average of all values = (Sum of values) ÷ (Number of values)
- Median: Middle value of the ordered data
- Mode: Value that occurs most frequently
Solved Problems
Problem 1: Find the mean of 4, 6, 10, 14, 16
Solution:
Sum = 4 + 6 + 10 + 14 + 16 = 50 Number of observations = 5
Mean = 50 ÷ 5 = 10
Mean = 10
Problem 2: Find the median of 3, 7, 5, 9, 11
Solution:
Arrange data in ascending order: 3, 5, 7, 9, 11
Middle value = 7
Median = 7
Problem 3: Find the mode of 2, 4, 6, 4, 8, 4, 10
Solution:
The number 4 occurs most frequently.
Mode = 4
Problem 4: The mean of 5 numbers is 20. Find their sum.
Solution:
Mean = Sum ÷ Number
Sum = Mean × Number = 20 × 5 = 100
Sum = 100
Problem 5: Find the median of 6, 8, 10, 12, 14, 16
Solution:
Data in order: 6, 8, 10, 12, 14, 16
Number of terms is even.
Median = (10 + 12) ÷ 2 = 11
Median = 11
Problem 6: The mean of 10 observations is 15. If 5 is added to each observation, find the new mean.
Solution:
Adding 5 to each value increases the mean by 5.
New Mean = 15 + 5 = 20
New Mean = 20
Problem 7: Find the mode of the data: 1, 2, 2, 3, 3, 3, 4
Solution:
The number 3 appears the maximum number of times.
Mode = 3
Problem 8: If the median of 7, x, 9 is 8, find x.
Solution:
Arranging the data: 7, x, 9
Median = middle value = x
Given median = 8
x = 8
Exam Tips
✔ Always arrange data before finding median
✔ Mean changes when values are added or removed
✔ Mode may be more than one or may not exist
Common Mistakes
- Forgetting to order data for median
- Dividing by incorrect number of observations
- Confusing mean and median
- Assuming mode always exists
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