Grouped Data Standard Deviation Calculator
Calculate mean, variance, and standard deviation for grouped frequency data
Enter Frequency Distribution Data
Data Ranges
Range 1
Range 2
Enter frequency distribution data above to calculate statistics
Example: Coffee Calorie Analysis
Coffee Drink Calories (30 observations)
Range (kcal) | Frequency | Midpoint |
---|---|---|
100-129 | 5 | 114.5 |
130-159 | 4 | 144.5 |
160-189 | 12 | 174.5 |
190-219 | 6 | 204.5 |
220-249 | 3 | 234.5 |
Results
Mean: 172.5 kcal
Standard Deviation: 36 kcal
Interpretation: On average, coffee drinks contain 172.5 kcal, with typical variation of ±36 kcal
Key Concepts
Midpoint
Average of range endpoints
M = (min + max) / 2
Grouped Mean
Weighted average using frequencies
μ = Σ(Mi×Fi) / n
Standard Deviation
Measure of data spread
σ = √variance
Calculation Steps
Find midpoint of each range
Sum all frequencies (sample size)
Calculate weighted mean
Compute variance using formula
Take square root for std deviation
Understanding Grouped Data Standard Deviation
What is Grouped Data?
Grouped data is organized into ranges or intervals with associated frequencies, rather than individual data points. This organization makes it easier to analyze large datasets and identify patterns in the distribution.
Why Use Grouped Data?
- •Simplifies analysis of large datasets
- •Reveals distribution patterns clearly
- •Facilitates frequency distribution analysis
- •Enables histogram creation
Mathematical Formulas
Mean Formula
μ = Σ(Mi × Fi) / n
Where Mi = midpoint, Fi = frequency, n = total frequency
Variance Formula
σ² = [Σ(Fi × Mi²) - n × μ²] / (n - 1)
Sample variance formula (n-1 in denominator)
Standard Deviation
σ = √(variance)
Square root of variance