Comprehensive Calculator Guide
This calculator gives the mean, standard deviation and variance of data in a frequency table, from class midpoints and frequencies. Thirty marks in classes centred on 55, 65, 75, 85, 95 with frequencies 3, 7, 12, 6, 2 have a mean of 74 and an SD of 10.44.
Grouped data
Mean = Σfx ÷ Σf; SD = √(Σf(x − x̄)² ÷ Σf) for a population or ÷ (Σf − 1) for a sample. Each class is assumed to sit at its midpoint, so the result is an estimate.
How to Use
- Enter the midpoints.
- Enter the frequencies and choose sample or population.
- Press “Calculate” to see the SD, mean and table.
Formula Used
x̄ = Σfx ÷ Σf | σ = √(Σf(x − x̄)² ÷ Σf)
Practical Examples
- Example 1
- Marks: mean 74, SD 10.44.
- Example 2
- Ages: mean 30.25, SD 11.76.
Important Tips
- One frequency per class.
- Check the total.
- Verify with Σfx²/Σf − x̄².
Common Mistakes to Avoid
- Using class limits.
- Dividing by the number of classes.
- Forgetting the frequency.
Frequently Asked Questions
- Grouped data?
- Data in classes with counts.
- Midpoint?
- Half the sum of the limits.
- Exact?
- An estimate.