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.

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