Question 1Easier
A box contains 6 cards labeled 2, 3 cards labeled 10, and 1 card labeled 20. A card is drawn at random. What is the expected value of the number on the card?
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Answer: B — 6.2
The expected value is .
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Mathematics
Measures of center and spread — ACT practice questions
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What this topic is
Mean, median and mode describe the center of a data set, while range and standard deviation describe how spread out it is; together they form Measures of center and spread.
One outlier shows the difference clearly: replacing the largest value with a much larger one raises the mean but leaves the median unchanged. ACT questions also run the mean backward, giving an average and asking for a missing value, which is easiest to find from the total.
Expected value appears too, as a probability-weighted average of outcomes. Answer choices for effect questions are often short statements about whether the mean and median increase, decrease or stay the same.
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Question 2Easier
A bakery recorded its muffin sales for 6 days: 20, 35, 40, 50, 15, and 45. On the seventh day, sales were muffins. The mean daily sales over all 7 days was 33 muffins. What is the value of ?
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Answer: B — 26
The six known values sum to 205. For a mean of 33 over 7 days, the total must be 231, so .
Question 3Easier
A lab recorded five reaction times, in milliseconds: 14, 27, 31, 40, and 48. One measurement is later corrected: the entry 48 is replaced by 98. Which of the following statements correctly describes the effect of this replacement on the mean and the median?
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Answer: D — The mean increases, and the median stays the same.
The original ordered list is 14,27,31,40,48 (median 31). Replacing 48 with 98 yields 14,27,31,40,98, so the median remains 31. The total increases by 50, so the mean increases by .
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More ACT topics
Mathematics
- Real number system and number properties
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Polynomial expressions and factoring
- Quadratic equations
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
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