Grouped Data Calculations
Ages 16–18Difficulty adapts to you
Grouped Data Calculations
For each class, calculate midpoint m = (lower boundary + upper boundary) ÷ 2. The estimated mean is x̄ ≈ Σfm ÷ Σf. For grouped median, use Median ≈ L + ((N ÷ 2 − cf) ÷ f)h; for grouped quartiles use N ÷ 4 and 3N ÷ 4. The grouped mode can be estimated with L + ((f₁ − f₀) ÷ (2f₁ − f₀ − f₂))h. The data inside a class is unknown, so these results are estimates. Use class boundaries carefully when intervals are inclusive.
Your goals
- ✓You can estimate statistics from a grouped frequency table using class intervals and midpoints.
- ✓You can use Grouped Data Calculations, model correctly.
- ✓You can use the definitions, units, assumptions, and examples to check your answer.
Words to know
- Grouped Data Calculations:
- Estimate statistics from a grouped frequency table using class intervals and midpoints.
- model:
- A rule or representation used to describe a situation and make a prediction.
Examples
- 1For classes 0–10, 10–20, 20–30 with frequencies 2, 5, 3, the midpoints are 5, 15, 25; Σf = 10 and Σfm = 10 + 75 + 75 = 160, so x̄ ≈ 16.
- 2The modal class is the class with the greatest frequency, while the exact mode is not known from grouped data alone.
Check these
- • Do not skip the meaning of a term or give a result without explaining what it means.
- • Keep every number, symbol, label, and unit in its correct place.
- • Show enough working to check how you reached your answer.
Helpful habits
- • Read the whole question before choosing what to do.
- • Show one clear step at a time and check each step.
- • If you are stuck, draw a model, try smaller numbers, or revisit the example.
Now try your own
Create your own grouped data calculations example, solve it, and explain how you checked it.
Professor Wise Owl
Wisdom & Understanding“Mistakes are proof that you are trying. Keep going!”