Discover the power of statistical measures! Learn to calculate and interpret mean, median, mode, range, and standard deviation to unlock insights from data.
Mean (Average): Sum of all values ÷ number of values
Median: Middle value when data is ordered
Mode: Most frequently occurring value
Range: Maximum value - minimum value
Standard Deviation: Measure of data spread
Variance: Average of squared deviations
Data: 85, 92, 78, 96, 88, 91, 83, 89, 94, 87
Step 1: Add all values
85 + 92 + 78 + 96 + 88 + 91 + 83 + 89 + 94 + 87 = 883
Step 2: Count the number of values
Number of values = 10
Step 3: Calculate the mean
Mean = 883 ÷ 10 = 88.3
Interpretation: The average test score is 88.3 points
Problem: A student's grades are: Tests (80%, weight 60%), Homework (95%, weight 30%), Participation (90%, weight 10%)
Step 1: Multiply each grade by its weight
Tests: 80 × 0.60 = 48
Homework: 95 × 0.30 = 28.5
Participation: 90 × 0.10 = 9
Step 2: Add the weighted scores
48 + 28.5 + 9 = 85.5
Result: Weighted mean = 85.5%
Data: 12, 15, 18, 20, 22, 25, 28, 30, 35
Step 1: Data is already ordered (9 values)
12, 15, 18, 20, 22, 25, 28, 30, 35
Step 2: Find the middle position
Middle position = (9 + 1) ÷ 2 = 5th position
Step 3: Identify the median
Median = 22 (the 5th value)
Data: 3, 5, 7, 5, 9, 5, 2, 7, 5, 1
Step 1: Count frequency of each value
Step 2: Identify the most frequent value
Mode = 5 (appears 4 times)
Data: 45, 52, 38, 61, 47, 55, 42, 58, 49, 51
Step 1: Find maximum and minimum values
Maximum = 61
Minimum = 38
Step 2: Calculate range
Range = 61 - 38 = 23
Interpretation: The data spans 23 units
Data: 2, 4, 6, 8, 10
Step 1: Find the mean
Mean = (2 + 4 + 6 + 8 + 10) ÷ 5 = 6
Step 2: Calculate deviations from mean
Step 3: Square the deviations
Step 4: Calculate variance and standard deviation
Variance = (16 + 4 + 0 + 4 + 16) ÷ 5 = 8
Standard Deviation = √8 ≈ 2.83
Class A: 85, 87, 89, 91, 93 (Mean = 89, Range = 8)
Class B: 70, 80, 90, 100, 110 (Mean = 90, Range = 40)
Analysis:
Conclusion: Class A is more consistent, Class B has higher average but more spread
Always arrange data in ascending order before finding the median
Mean is the average, median is the middle value - they can be very different
Extreme values can significantly affect the mean but not the median
Problem 1:
Find the mean, median, and mode of: 12, 15, 18, 15, 20, 12, 15
Mean: 107 ÷ 7 = 15.3
Median: 15 (middle value when ordered)
Mode: 15 (appears 3 times)
Problem 2:
Calculate the range of: 25, 30, 35, 40, 45, 50, 55
Range = 55 - 25 = 30
Problem 3:
Which measure is most affected by outliers: mean, median, or mode?
The mean is most affected by outliers because it includes all values in its calculation.
Formula:
Weighted Mean = Σ(w × x) / Σw
Example: Grade calculation with different test weights
Key Measures:
Q1 (25%), Q2 (50%), Q3 (75%)
Use: Understanding data distribution and spread
Market Analysis
Stock price trends and volatility
Customer satisfaction surveys and quality control
Clinical Trials
Drug effectiveness and side effects
Patient vital signs monitoring and diagnosis
Machine Learning
Model performance evaluation
User behavior analysis and A/B testing