questionTest1Part1Spring2025

Sample Questions for Test I, Part I

1. Frequency and Relative Frequency

• Frequency: The number of times a data point appears in a dataset.

• Relative Frequency: The frequency of a particular value compared to the total number of observations, expressed as a fraction or percentage.

2. Class Mark and Class Boundaries

• Class Mark: The midpoint of a class interval.

• Class Boundaries: The values that define the limits of classes in grouped data.

3. Class Width

• Class Width: The difference between the upper and lower boundaries of a class.

4. Visual Representation of Frequencies

• For displaying grouped frequencies, use bar chart for clear comparisons instead of a pie chart which shows parts of a whole.

5. Mean Calculation

• Given data: 1, 3, 5, 9, 6, 8, 3

• Mean = (1 + 3 + 5 + 9 + 6 + 8 + 3)/7 = 5

6. Median Calculation

• Given sorted data: 1, 3, 3, 4, 5, 6, 8, 9

• Median = (4 + 5) / 2 = 4.5

7. Range Calculation

• Given the data: 3, 4, 4, 5, 7, 8, 9, 9, 23400

• Range = Maximum - Minimum = 23400 - 3 = 23397

8. Outliers Impact

• Outlier in data affects the mean significantly more than it does the median.

9-10. Sample Variance and Standard Deviation

• Given: n = 2, S xi = 5, S xi^2 = 17

• Sample Variance (s²) = (17 - 12.5) / 1 = 4.5

• Sample Standard Deviation (s) = √s² = 2.121 (if calculated).

11-12. Proportion of Data Within Standard Deviations

• Approx. 95% of data lies within 2 standard deviations.

• Approx. 99% of data lies within 3 standard deviations.

13. Quartiles Calculation

• Given sorted data: 1, 3, 3, 4, 5, 6, 8, 9

• Q1 (25th percentile) = 3; Q3 (75th percentile) = 7.

14. Data Extremes

• Extremes = Minimum and Maximum values = 1 and 9.

15. Boxplot

• To draw the boxplot, plot the quartiles and extremes based on the data in question 6.

16. Population Mean vs Sample Mean

• Population Mean: Average of the entire population.

• Sample Mean: Average calculated from a sample of the population.

17. Types of Data

• The state of birth of a group of students is (b) Qualitative data.

18. Stem-and-Leaf Display

• Given data: {10, 7, 12, 5, 7, 21, 3, 9, 9, 12, 1, 10, 13, 4}

• Stem of Five:

  • 0 | 134

  • 0 | 57799

  • 1 | 00223

  • 1 | 2

19. Five Number Summary

• Given data from Question 18: 1, 5, 9, 12, 21

20. Boxplot for Data in Question 18

• Draw a boxplot using the five-number summary from question 19.

Page 2 Questions

21. Mean and Standard Deviation

• Data from question 18: Mean = 8.785714; Standard Deviation = 5.025758

22. Sample Size and Standard Deviations

• In a sample of size 125, 89% of data is within 3 standard deviations, approx. 111 observations.

23. Sample Size Calculation

• Possible samples (size 2) from 5 employees = 10 (5C2 = 5*4/2!)

24. Sample Mean Robustness

• The sample mean is not robust against outliers, as it is directly affected by their presence.

25. Independent Events

• Two events A and B are independent if and only if P(A|B) = P(A).

26. Probability Statement

• Probability P(pass) = 1.1 is incorrect because probabilities must range from 0 to 1.

27. P(A or B) Calculation

• P(A or B) = P(A) + P(B) - P(A and B) = 0.5 + 0.7 - 0.3 = 0.9

28-29. Event Independence and Exclusivity

• A and B are not independent as P(AB) = 0.3 does not equal P(A)P(B) = 0.35.

• A and B are not mutually exclusive because they can occur simultaneously.

30. Complement Probability

• P(Ac) = 1 - P(A) = 1 - 0.5 = 0.5

31. Complement Probability

• P(Ac and Bc) = 1 - P(A or B) = 0.1

32-41. Sample Space of Random Phenomena

• Toss a coin twice: Sample Space = {H,T}

• Random student selection: S = {List of students}

• Random assignment of clients: Three ways as per the number of clients and salespersons.

• Sum of dice to be 10, odds, etc., and probabilities when rolling two dice computed using standard methods.

Page 3 Questions

42. Independent Events Probability

• For independent A and B: P(A and B) = P(A) * P(B).

43. Independence and Exclusivity

• Independent events cannot be mutually exclusive; they can occur together.

44. Left-handed Students Probability

• Probability of choosing 2 left-handed students out of 10.

45-46. Factorials and Combinations

• 5! = 120 (orderings of 5 people).

• 7C5 = 21 (ways to choose 5 out of 7).

47. Medals Distribution

• Medals distribution ways: 8! / (8-3)! = 336.

48-49. Probability Determinations on Dice Rolls

• Probabilities calculated for sums, evenness, etc., based on outcomes for pairs of rolled dice.

Page 4 Questions

Emission Control Unit Testing (Problem 1)

• Histogram of CO2 emissions data derived from vehicle testing conducted on Sept 30, 1997.

• Compare groups of vehicles using boxplots.

Stats Class Grades (Problem 2)

• Plot final grades distribution in a class with Business and Engineering majors.

• Events and their probabilities analyzed based on students' performance.

Profit Data from 10 Companies (Problem 3)

• Stem and leaf diagrams constructed to analyze company profits, further insights provided based on gathered data.