STATS SLEUTH EXAM

Quarter 3 Comprehensive • Statistics & Probability

NAME:

DATE:

Carefully read each question. For each item, select the best answer and mark it clearly. Use a calculator for calculations where appropriate. Ensure your final answers are based on standard statistical definitions.

Section 1: Measurement & Sampling

1. Which level of measurement applies to "Colors of sports cars in a showroom"?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

2. Which level of measurement applies to "The top 5 rankings of the world's fastest runners"?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

3. Which level of measurement applies to "Temperature measured in degrees Fahrenheit"?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

4. Which level of measurement applies to "The weight of newborns in a hospital"?

A) Nominal

B) Ordinal

C) Interval

D) Ratio

5. A researcher selects every 15th person entering a stadium. What sampling method is this?

A) Stratified

B) Systematic

C) Cluster

D) Convenience

6. A town is divided into 10 precincts. A researcher selects all residents from 3 precincts to survey. This is:

A) Stratified

B) Random

C) Cluster

D) Systematic

7. A study divides a college by major and selects 20 students from each major. What sampling method is this?

A) Convenience

B) Cluster

C) Stratified

D) Random

8. Using a computer to generate 50 unique student ID numbers is an example of what sampling?

A) Simple Random

B) Systematic

C) Stratified

D) Convenience

9. Interviewing the first 25 people who walk into a grocery store is known as:

A) Cluster Sampling

B) Systematic

C) Convenience

D) Random

10. A "Parameter" is a numerical description of a ______, while a "Statistic" describes a ______.

A) Sample; Population

B) Population; Sample

C) Variable; Constant

D) Mean; Median

11. The number of siblings a person has is an example of what type of variable?

A) Continuous

B) Discrete

C) Qualitative

D) Nominal

12. Which of the following is a quantitative variable?

A) Eye Color

B) Zip Code

C) Annual Salary

D) Religious Affiliation

13. The level of measurement for "Social Security Numbers" is:

A) Nominal

B) Ordinal

C) Interval

D) Ratio

Section 2: Distributions & Histograms

14. To find the class midpoint, you should:

A) Average lower/upper limits

B) Subtract limits

C) Add 0.5 to upper limit

D) Use the frequency

15. What is the class width for a distribution with classes 10–19, 20–29, 30–39?

A) 9

B) 10

C) 19

D) 20

16. The lower class boundary for the class 15–24 is:

A) 14

B) 14.5

C) 15

D) 15.5

17. Relative frequency is calculated by dividing ______ by the ______.

A) Class width; Limit

B) Frequency; Total

C) Total; Frequency

D) Boundary; Midpoint

18. A histogram that has a long tail on the right side is said to be:

A) Symmetrical

B) Skewed Right

C) Skewed Left

D) Uniform

19. In a frequency table, the sum of all relative frequencies should be approximately:

A) 0

B) 0.5

C) 1.0

D) 100

20. Which type of graph uses midpoints on the horizontal axis and frequencies on the vertical?

A) Ogive

B) Pie Chart

C) Frequency Polygon

D) Stem-and-leaf

21. What value represents the sum of the frequencies for that class and all previous classes?

A) Relative Frequency

B) Cumulative Frequency

C) Midpoint

D) Sample Mean

22. If a histogram bar for class 20–29 has a frequency of 15 out of 50, its relative frequency is:

A) 0.15

B) 0.30

C) 0.45

D) 0.60

23. A Pareto chart is a bar graph where the bars are arranged in:

A) Ascending order

B) Descending order

C) Alphabetical order

D) Random order

24. For the class 40–49, what is the midpoint?

A) 44

B) 44.5

C) 45

D) 45.5

25. An ogive is a graph that displays ______ frequencies.

A) Relative

B) Cumulative

C) Raw

D) Expected

26. A bimodal distribution has how many peaks?

A) 1

B) 2

C) 3

D) 4

Section 3 Begins on Next Page: Central Tendency & Variation

Section 3: Variation & Distribution

27. What is the range of breaking strengths (lbs): 10.1, 6.2, 9.8, 5.3, 9.9, 5.7?

A) 4.8

B) 5.3

C) 10.1

D) 7.8

28. The sample standard deviation measures what characteristic of the data?

A) Middle of data

B) Avg distance from mean

C) Most frequent value

D) Total spread

29. Sample A (Mean 10, SD 2) vs Sample B (Mean 100, SD 10). Which has higher CV?

A) Sample A (20%)

B) Sample B (10%)

C) Both equal

D) Cannot determine

30. To calculate Sample Variance (\(s^2\)), divide the sum of squared deviations by:

A) \(n\)

B) \(n - 1\)

C) \(n + 1\)

D) \(\sqrt{n}\)

31. A sample has \(\bar{x} = 7.8\) and \(s = 2.3\). Calculate the Coefficient of Variation (CV).

A) 29.5%

B) 34.1%

C) 23.0%

D) 78.0%

32. In a box-and-whisker plot, the box itself represents which part of the data?

A) Entire range

B) Middle 50% (IQR)

C) Lower 25%

D) Mean to max

33. Given the five-number summary [45, 67, 78, 87, 101], what is the IQR?

A) 56

B) 20

C) 11

D) 34

34. Which value in the five-number summary represents the 75th percentile?

A) Low Value

B) Median (Q2)

C) Q1

D) Q3

35. A sample of radon levels is: 1.9, 2.8, 5.7, 4.2, 1.9, 8.6, 3.9, 7.2. What is the mode?

A) 1.9

B) 4.05

C) 4.52

D) No mode

36. Chebyshev's Theorem states the proportion within \(k\) standard deviations is at least:

A) \(1 - (1/k)\)

B) \(1 - (1/k^2)\)

C) \(1/k^2\)

D) \(1 - k^2\)

37. At least what percentage of data falls within 2 standard deviations of the mean per Chebyshev?

A) 50%

B) 75%

C) 88.9%

D) 95%

38. If \(\bar{x} = 79\) and \(s = 10\), what is the 75% Chebyshev interval?

A) 69 to 89

B) 59 to 99

C) 49 to 109

D) 74 to 84

39. At least 88.9% of data falls within how many standard deviations (\(k\)) of the mean?

A) 2

B) 3

C) 4

D) 5

Section 4: Probability & Counting

40. If \(P(A) = 0.24\) and \(P(B|A) = 0.45\), what is \(P(A \text{ and } B)\)?

A) 0.69

B) 0.108

C) 0.21

D) 0.533

41. Two cards are drawn from a 52-card deck WITH replacement. Probability both are hearts?

A) 1/16

B) 1/17

C) 1/4

D) 1/26

42. Two cards are drawn WITHOUT replacement. Probability both are hearts?

A) 1/16

B) 3/51

C) 1/17

D) 13/204

43. A fair die is rolled. What is the probability of rolling a number less than 3?

A) 1/6

B) 1/3

C) 1/2

D) 2/3

44. Drop 500 thumbtacks; 340 land flat. What is the relative frequency probability of landing flat?

A) 0.34

B) 0.50

C) 0.68

D) 0.16

45. Two events are mutually exclusive if:

A) One changes other

B) Can't happen at same time

C) Sum to 1

D) Are independent

46. How many sequences are possible for a 5-question 4-option quiz?

A) 20

B) 625

C) 1024

D) 540

47. Compute \(P_{7,2}\) (Permutations of 7 items taken 2 at a time).

A) 14

B) 21

C) 42

D) 49

48. Compute \(C_{7,2}\) (Combinations of 7 items taken 2 at a time).

A) 14

B) 21

C) 42

D) 49

49. A council of 8 chooses 2 to attend a meeting. How many different pairs can be selected?

A) 16

B) 28

C) 56

D) 64

50. What is the value of \(0!\) (zero factorial)?

A) 0

B) 1

C) Undefined

D) -1

Optional Scratch Space

Stats Sleuth Comprehensive

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Statistics Quarterly Exam Answer Key

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