Grouped Data Standard Deviation Calculator

Calculate mean, variance, and standard deviation for grouped frequency data

Enter Frequency Distribution Data

Data Ranges

Range 1

Enter min and max values to see midpoint

Range 2

Enter min and max values to see midpoint

Enter frequency distribution data above to calculate statistics

Example: Coffee Calorie Analysis

Coffee Drink Calories (30 observations)

Range (kcal)FrequencyMidpoint
100-1295114.5
130-1594144.5
160-18912174.5
190-2196204.5
220-2493234.5

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

M

Midpoint

Average of range endpoints

M = (min + max) / 2

μ

Grouped Mean

Weighted average using frequencies

μ = Σ(Mi×Fi) / n

σ

Standard Deviation

Measure of data spread

σ = √variance

Calculation Steps

1.

Find midpoint of each range

2.

Sum all frequencies (sample size)

3.

Calculate weighted mean

4.

Compute variance using formula

5.

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