Quiz: Fundamentals of Data and Geometry — 20 questions

1. In a stem and leaf plot, what does the leaf represent?

A. The leading digits used to group the data

B. The frequency of values in each row

C. The largest value in the data set

D. The remaining digit or digits for each value

Answer: (D)

Explanation

The leaf is the part of the value written beside the stem, usually the units digit or digits. The stem groups the values by their leading digits.

2. Why are leaves usually written in increasing order within each stem row?

A. To make the plot easier to read quickly

B. To change the median of the data

C. To show the frequency of each stem

D. To separate repeated values into different rows

Answer: (A)

Explanation

Ordered leaves let the data be read left to right in size order. This makes the plot quicker to interpret.

3. What feature of a histogram shows that the data are continuous rather than separate categories?

A. The bars touch each other

B. The bars are drawn with gaps between them

C. The x-axis is hidden

D. The bars all have the same height

Answer: (A)

Explanation

Histogram bars touch because each class interval covers a continuous range of values with no gaps. Gaps would suggest separate categories, not continuous data.

4. When class widths are different in a histogram, what must be used so that bar area represents frequency correctly?

A. Median

B. Range

C. Cumulative count

D. Frequency density

Answer: (D)

Explanation

With unequal class widths, frequency density is used so that the area of each bar matches the frequency. Using height alone would give misleading results.

5. Which measure of center is the middle value after the data have been ordered?

A. Range

B. Mean

C. Median

D. Mode

Answer: (C)

Explanation

The median is the central value in an ordered data set. If there is an even number of values, it is found by averaging the two middle values.

6. What is true if a data set has more than one value tied for the highest frequency?

A. It is multimodal

B. Its mean must equal its median

C. It has no mode

D. Its median must be the largest value

Answer: (A)

Explanation

A data set with multiple most-frequent values is multimodal. The mode is the value, or values, that occur most often.

7. How is the interquartile range calculated?

A. Q3 minus Q1

B. Median minus minimum

C. Mean minus median

D. Maximum minus minimum

Answer: (A)

Explanation

The interquartile range is the spread between the first quartile and the third quartile, so IQR = Q3 − Q1. It measures the spread of the middle 50% of the data.

8. In a box plot, which values are shown by the ends of the box?

A. First quartile and third quartile

B. Lower whisker and upper whisker

C. Mean and median

D. Minimum and maximum

Answer: (A)

Explanation

The box itself runs from Q1 to Q3, so its edges show the lower and upper quartiles. The line inside the box shows the median.

9. What does a Venn diagram use to represent events and their overlaps?

A. Overlapping circles

B. A number line from 0 to 1

C. Branches from a starting point

D. Separate bars

Answer: (A)

Explanation

Venn diagrams show events using overlapping circles, which makes intersections easy to see. A tree diagram is the representation that uses branches.

10. What happens to probabilities along one path in a tree diagram for a multi-step experiment?

A. They are always equal to 1

B. They are placed in ascending order

C. They are multiplied together

D. They are added together

Answer: (C)

Explanation

In a tree diagram, probabilities along a single path are multiplied to find the probability of that combined outcome. This is how multi-step events are calculated.

11. What is the probability of the complement of an event with probability 0.32?

A. 0.32

B. 0.18

C. 0.68

D. 1.32

Answer: (C)

Explanation

The complement is found by subtracting the event probability from 1, so 1 - 0.32 = 0.68. The value 0.32 is the original event probability, not its complement.

12. If two events are mutually exclusive, which rule is used to find the probability that either event occurs?

A. Add their probabilities

B. Subtract one probability from the other

C. Divide one probability by the other

D. Multiply their probabilities

Answer: (A)

Explanation

Mutually exclusive events cannot happen together, so the probability of A or B is P(A) + P(B). Multiplication is used for independent events, not mutually exclusive ones.

13. Which expression represents a square number?

A. n ÷ n

B. n - n

C. n × n

D. n + n

Answer: (C)

Explanation

A square number is written as n squared, meaning n multiplied by itself. The other expressions do not represent repeated multiplication.

14. What is the prime factor form of 18?

A. 3 × 6

B. 1 × 18

C. 2 × 3 × 3

D. 2 × 9

Answer: (C)

Explanation

Prime factorization breaks a number into only prime factors, and 18 = 2 × 3 × 3. The other choices still include non-prime factors or are not a prime factorization.

15. In a right-angled triangle, which side is the hypotenuse?

A. The side opposite the smallest angle

B. The side opposite the 90° angle

C. The shortest side

D. The side that meets the 90° angle

Answer: (B)

Explanation

The hypotenuse is the side opposite the 90° angle, and it is the longest side. The two sides meeting at the right angle are the legs.

16. A right triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?

A. 14 cm

B. 12 cm

C. 10 cm

D. 2 cm

Answer: (C)

Explanation

Using Pythagoras’ theorem, c^2 = 6^2 + 8^2 = 36 + 64 = 100, so c = 10 cm. The other options come from incorrect arithmetic or rule use.

17. What is the sum of the interior angles of a quadrilateral?

A. 360°

B. 540°

C. 270°

D. 180°

Answer: (A)

Explanation

A quadrilateral has four sides, and its interior angles add to 360°. A triangle, by contrast, has an interior angle sum of 180°.

18. How do you find each interior angle of a regular polygon?

A. Multiply the angle sum by the number of sides

B. Subtract 180° from the angle sum

C. Divide 180° by the number of sides

D. Divide the angle sum by the number of sides

Answer: (D)

Explanation

For a regular polygon, each interior angle is the total interior angle sum divided by the number of sides. This works because all angles are equal in a regular polygon.

19. What is true of similar shapes?

A. Their corresponding angles are equal and side lengths are proportional

B. They must be congruent

C. Their area must be the same

D. Their side lengths are equal and angles are different

Answer: (A)

Explanation

Similar shapes have the same angles and proportional corresponding sides. They do not have to be the same size, so they are not necessarily congruent.

20. In a right triangle, which trigonometric ratio is opposite divided by hypotenuse?

A. Tangent

B. Cotangent

C. Cosine

D. Sine

Answer: (D)

Explanation

Sine is defined as opposite over hypotenuse. Cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.