Flashcards · 4MA1 · Topic 6

Statistics and probability flashcards

18 cards on Topic 6, subtopics 6.1 to 6.3. Pick a subtopic or study them all.

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Pie chart: 12 of 45 people chose "walk". Find the sector angle.: Angle = (frequency ÷ total) × 360° = 12/45 × 360° = 96°.
Bar charts and pictograms: key rules: Bar charts for categories have equal widths and gaps between bars. Pictograms need a key.
How do you complete a two-way table?: Every row and column must add to its total. Fill the cell that is missing only one value first, then repeat.
HistogramsHigher: No gaps, a continuous scale on the horizontal axis, and frequency density on the vertical axis. Area represents frequency.
The class 20 < x ≤ 35 has frequency 24. Find its frequency density.Higher: Class width = 35 − 20 = 15. Frequency density = frequency ÷ class width = 24 ÷ 15 = 1.6.
Cumulative frequency graphsHigher: Plot running totals at upper class boundaries, starting at the lower boundary with 0; the graph never goes down.

Mean, median and mode: one strength or weakness of each: Mean: uses every value; affected by extreme values. Median: the middle value; not affected by extreme values. Mode: the only average for non-numerical data; there can be more than one.
Mode and modal class: Mode: a single value, for discrete data. Modal class: a class, for grouped data. Give the value or class, not its frequency.
Estimate the mean: 0 < x ≤ 4 (frequency 3), 4 < x ≤ 8 (5), 8 < x ≤ 12 (2): Midpoints 2, 6, 10. (3 × 2 + 5 × 6 + 2 × 10) ÷ 10 = 56 ÷ 10 = 5.6 It is an estimate, because midpoints replace the real values.
The mean of five numbers is 12. Four of them are 10, 14, 9 and 15. Find the fifth.: Total = 5 × 12 = 60. The four add to 48, so the fifth is 12.
Find the interquartile range of 2, 4, 5, 7, 8, 10, 13Higher: n = 7. Lower quartile: (n + 1)/4 = 2nd value = 4. Upper quartile: 3(n + 1)/4 = 6th value = 10. IQR = 10 − 4 = 6
Range and interquartile rangeHigher: Range uses the two extreme values. The IQR (upper quartile − lower quartile) measures the spread of the middle half and ignores extremes.

Outcome, event and sample space: Outcome: one possible result. Event: one or more outcomes. Sample space: the list of all outcomes.
Mutually exclusive events: Events that cannot happen together. For them, P(A or B) = P(A) + P(B).
Independent eventsHigher: One does not affect the other. P(A and B) = P(A) × P(B). Example: P(A) = 0.6, P(B) = 0.3 gives P(A and B) = 0.18.
Relative frequency and expected frequency: Relative frequency = times the event occurs ÷ number of trials; it is an estimate that improves with more trials. Expected frequency = probability × number of trials: P(win) = 0.15 in 240 games gives 36.
Two fair coins are thrown. Find P(at least one head).: Outcomes HH, HT, TH, TT; three contain a head: 3/4. (Or 1 − P(no heads) = 1 − 1/4.)
A bag has 4 green and 6 yellow sweets. Two are taken without replacement. Find P(both green).Higher: 4/10 × 3/9 = 12/90 = 2/15. On the second pick the denominator and the green numerator each go down by one.