Data & Probability
Histograms, frequency polygons and probability
Data Representation and Probability
Histograms show continuous data using joined bars. Frequency polygons connect midpoints of histogram bars. Probability measures the chance of an event: P(E) = favourable outcomes / total outcomes, where 0 ≤ P(E) ≤ 1.
Example
Histograms
Heights of learners (grouped data):
140–149 cm: 4 learners
150–159 cm: 8 learners
160–169 cm: 12 learners
170–179 cm: 6 learners
Draw bars with no gaps; height = frequency. The tallest bar (160–169) is the modal class.
Example
Calculating Probability
A bag has 3 red, 5 blue and 2 green marbles.
Total = 10
P(red) = 3/10
P(blue) = 5/10 = 1/2
P(not green) = 8/10 = 4/5
P(red or green) = (3+2)/10 = 1/2
Note
Remember
Probability: 0 = impossible, 1 = certain. P(not A) = 1 − P(A). In a histogram, bars touch (continuous data). In a bar graph, bars are separated (discrete data).
Key Vocabulary
HistogramA graph with joined bars showing continuous grouped data
Frequency polygonA line graph connecting midpoints of histogram classes
ProbabilityThe chance of an event happening (0 to 1)
OutcomeA possible result of an experiment
EventA set of one or more outcomes
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Histogram
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