Ungrouped Data Calculations
Ages 16–18Difficulty adapts to you
Ungrouped Data Calculations
For ungrouped data x₁, x₂, …, xₙ, the mean is x̄ = Σx ÷ n. After ordering the values, the median is the middle value for odd n and the mean of the two middle values for even n. The mode is the most frequent value and the range is maximum − minimum.
Your goals
- ✓You can calculate exact statistics from a list of individual observations.
- ✓You can use Ungrouped Data Calculations, model correctly.
- ✓You can use the definitions, units, assumptions, and examples to check your answer.
Words to know
- Ungrouped Data Calculations:
- Calculate exact statistics from a list of individual observations.
- model:
- A rule or representation used to describe a situation and make a prediction.
Examples
- 1For 3, 5, 5, 8, 9, x̄ = 30 ÷ 5 = 6, median = 5, mode = 5, and range = 9 − 3 = 6.
- 2For 4, 7, 10, 12, the median is (7 + 10) ÷ 2 = 8.5.
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 ungrouped data calculations example, solve it, and explain how you checked it.
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