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

B) Systematic

C) Convenience

D) Random

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

A) Sample; Pop.

B) Pop.; Sample

C) Var.; Const.

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) Religion

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) Avg limits

B) Subtract limits

C) Add 0.5

D) Use 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) Width; Limit

B) Freq; Total

C) Total; Freq

D) Bound.; Mid.

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 approx.:

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) Freq Polygon

D) Stem-and-leaf

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

A) Rel. Freq

B) Cum. Freq

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. In a probability tree diagram, the probability of an outcome at the end of a path is found by:

A) Adding

B) Subtracting

C) Multiplying

D) Dividing

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: 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

B) Avg dist mean

C) Most freq

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 det.

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 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%

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

Case Study: Probability Tree Analysis

A medical clinic treats patients for either a Cold (60%) or the Flu (40%). The probability of recovery within one week depends on the condition. Use the diagram below for items 36–39.

36. What is the probability that a patient has a cold AND recovers within a week?

A) 0.54

B) 0.60

C) 0.90

D) 0.15

37. What is the probability that a patient has the flu AND does NOT recover?

A) 0.28

B) 0.40

C) 0.12

D) 0.70

38. What is the total probability that a randomly selected patient recovers?

A) 0.82

B) 1.00

C) 0.54

D) 0.18

39. If a patient is known to have recovered, what is the probability they had a cold?

A) 0.540

B) 0.659

C) 0.900

D) 0.341

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. Prob. both hearts?

A) 1/16

B) 1/17

C) 1/4

D) 1/26

42. Two cards are drawn WITHOUT replacement. Prob. 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?

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 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 pairs?

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 Exam Document

Stats Sleuth Exam Document

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