ACT Preparation / Unit 15 ACT 1434 review, 2 to 3 minutes
One Class, Four Questions
The idea
Statistics and probability on the test ask four kinds of question. How were the data collected: a random sample represents its population, and a biased one does not, however large. What do the data look like: displays show the distribution, the mean, median and mode describe the center, and the range, IQR and standard deviation describe spread, with the median and IQR resisting outliers. How do two variables relate: a scatter plot shows association, a line of best fit predicts within the data, and correlation is not causation. And how likely is an event: favorable over total, complements for at least one, multiplication for independent events, addition with the overlap subtracted, and conditional probability restricted to the given group. Counting uses the multiplication principle, permutations when order matters and combinations when it does not.
In practice
Worked example: a teacher records quiz scores for 9 students: 62, 70, 74, 75, 78, 80, 84, 88, 97. The mean is 708/9, about 78.7, and the median is the 5th value, 78. The lower half, 62, 70, 74, 75, has the quartile (70 + 74)/2 = 72, and the upper half, 80, 84, 88, 97, has the quartile (84 + 88)/2 = 86, so the IQR is 14. No score lies more than 21 points beyond a quartile, so there are no potential outliers. A tenth student scores 40: the median becomes (75 + 78)/2 = 76.5, and the mean drops to 748/10 = 74.8. Choosing 2 of the original 9 to present together gives 9C2 = 36 pairs.
Where people slip
Three habits carry forward. Order data before finding medians and quartiles. Choose the denominator of a probability from the condition the question gives. And decide whether order matters before counting. This ends the mathematics; the next unit begins reading, with what a passage says and what it implies.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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