5. Summarizing Data: Averages, Spread & Probability

Science often boils a column of numbers down to a few summary values. The GED® expects you to compute them.

Mean (average): add all values, divide by how many there are.
\[ \text{mean} = \frac{\text{sum of values}}{\text{number of values}}. \]
For the measurements \(4, 8, 6, 2\): \(\frac{4+8+6+2}{4} = \frac{20}{4} = 5\).

Median: put the values in order and take the middle one. Mode: the most frequent value. Range: largest − smallest, a quick measure of spread.

Probability measures how likely an outcome is, from 0 (impossible) to 1 (certain):
\[ P(\text{event}) = \frac{\text{favorable outcomes}}{\text{total outcomes}}. \]

In genetics, for instance, a cross that gives 3 dominant to 1 recessive means \(P(\text{recessive}) = \frac{1}{4} = 0.25 = 25\%\).

⚠️ Common misconception: the mean can be pulled far off by one extreme value. When data has an outlier (one huge or tiny number), the median describes the 'typical' value better.

💡 Tip: always order the numbers before finding the median — forgetting to sort is the most common error.