Question 1
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?
- A5.6
- B6.2
- C8
- D10
Show answer
Answer: B — 6.2
The expected value is .
Study on the fly›ACT›Mathematics › Measures of center and spread
MathematicsFree
Measures of center and spread — ACT practice questions
Measures of center and spread on the ACT Mathematics test covers the mean, the median, and expected value, along with how replacing a data point changes those summaries. A student has to find a missing list value when the mean is given, compute the expected value of a card drawn at random, and judge the effect of correcting one measurement on both the mean and the median. Items are multiple choice: some ask for a single number, others offer statements about which measure moves. Common traps swap mean with median or ignore that an extreme replacement pulls the mean more than the median.
- Section: Mathematics 45 questions on the paper
- 56 practice questions in the app
Sample questions
Question 2
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 ?
- A20
- B26
- C33
- D36
Show answer
Answer: B — 26
The six known values sum to 205. For a mean of 33 over 7 days, the total must be 231, so m = 231 − 205 = 26.
Question 3
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?
- AThe mean stays the same, and the median stays the same.
- BThe mean stays the same, and the median increases.
- CThe mean increases, and the median increases.
- DThe mean increases, and the median stays the same.
Show answer
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 .
Practice 56 Measures of center and spread questions in the app
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
Study on the fly is an independent study tool and is not affiliated with, sponsored by, or endorsed by any testing organization, school, or government body.
ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, and does not endorse, this product.
All practice questions and passages are original works created for Study on the fly and are not reproduced from any official test.