Statistics Solved Examples (Class 10 Mathematics)
Analyze data using mean, median, mode, and standard deviation. These problems develop competence in data interpretation and statistical measures.
TL;DR: Analyze data using mean, median, mode, and standard deviation. These problems develop competence in data interpretation and statistical measures.
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Analyze data using mean, median, mode, and standard deviation. These problems develop competence in data interpretation and statistical measures.
Statistics — Solved Numerical Examples (Step by Step)
Example 1: Find the mean of the data: 10, 15, 20, 25, 30
Solution: Mean = (10 + 15 + 20 + 25 + 30) / 5 = 100 / 5 = 20
Example 2: Find the median of the data: 3, 7, 2, 9, 5, 1, 8
Solution: Arrange in ascending order: 1, 2, 3, 5, 7, 8, 9
Number of observations n = 7 (odd)
Median = middle observation = (n+1)/2 = 4th observation = 5
Example 3: Find the mode of the data: 4, 5, 5, 6, 6, 6, 7, 8, 8, 8, 8, 9
Solution: Frequency of 4: 1
Frequency of 5: 2
Frequency of 6: 3
Frequency of 7: 1
Frequency of 8: 4
Frequency of 9: 1
Mode = value with highest frequency = 8 (appears 4 times)
Example 4: The mean of five numbers is 12. Four of them are 10, 11, 13, 14. Find the fifth number.
Solution: Sum of five numbers = 5 × 12 = 60
Sum of first four numbers = 10 + 11 + 13 + 14 = 48
Fifth number = 60 - 48 = 12
Example 5: Find the range of the data: 15, 8, 22, 5, 18, 30, 12
Solution: Range = Maximum value - Minimum value
Maximum = 30, Minimum = 5
Range = 30 - 5 = 25
Example 6: The mean of 10 observations is 20. If each observation is increased by 5, what is the new mean?
Solution: Original mean = 20
Each observation increased by 5, so each new observation = old observation + 5
New mean = old mean + 5 = 20 + 5 = 25
Tips
- Mean is affected by extreme values; median is more robust for skewed distributions.
- Mode is the most frequent value; a dataset can have no mode, one mode, or multiple modes.
- When n is even, median = average of (n/2)th and (n/2 + 1)th observations.
Frequently Asked Questions
Why is the median sometimes preferred over the mean?
The median is not affected by extreme outliers. For skewed data, it represents the center better than the mean.
What happens to the mean if all data points are multiplied by a constant k?
The new mean = old mean × k. This is because the sum is multiplied by k, and division by n still gives k times the original mean.
More Mathematics Solved Examples
- Real Numbers (HCF LCM Euclid)
- Pair of Linear Equations in Two Variables
- Circles
- Statistics
- Linear Equations in Two Variables
- Heron's Formula
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