University:
York University
Course:
MATH 1131 | Introduction to Statistics I
Academic year:

2022
Views:

38

Pages:

4
Author:

Niklas

Exercise 4 Data: Bar Ingegneria: 1 1 2 2 3 3 3 4 4 5 Bar H3: 2 2 3 3 3 4 4 5 5 Calculations: Bar Ingegneria Mean: (1+1+2+2+3+3+3+4+4+5) / 10 = 2.6 Median: 5th position = 3 Variance: σ² = 1.14 Five-number summary: Q₁ = 1.5 Q₂ = 3 Q₃ = 3.5 IQR = Q₃ - Q₁ = 2 Uω = Q₃ + 1.5IQR = 6.5 Lω = Q₁ - 1.5IQR = -1.5 Bar H3 Mean: (2+2+3+3+3+4+4+5+5) / 9 = 3.2 Median: 5th position = 3 Variance: σ² = 1.28 Five-number summary: Q₁ = 2.5 Q₂ = 3 Q₃ = 4.5 IQR = Q₃ - Q₁ = 2 Uω = Q₃ + 1.5IQR = 8.25 Lω = Q₁ - 1.5IQR = -1.75 Exercise 5 Data: A table showing the number of hours students spend studying daily, grouped into intervals. Calculations: Mean: H = (14 + 313 + 522 + 76 + 93 + 112) / 50 = 4.88 ≈ 5 Percentages: Less than 4 hours: (13+4) / 50 * 100 = 34% More than 5 hours: (22+6+3) / 50 * 100 = 62% Between 1 and 10 hours: (13+22+6+3) / 50 * 100 = 86% Exercise 6 The quantity Σ(xi - x̄) is not used as a measure of dispersion because it is: X always equal to zero Exercise 7 Data: A table showing the frequency distribution of storm durations. Calculations: Median: M = 37 Approximate mean: The median is contained within the fourth interval (75-100). The exact mean cannot be computed from the grouped data. Histogram: A histogram is drawn with the x-axis representing the storm duration and the y-axis representing the frequency. The bars are labeled with the intervals and the height of each bar corresponds to the number of storms in that interval. a. Which distribution's mean differs from the mean of the other two distributions? The mean of distribution C differs from the means of distributions A and B. b. Is it likely that the mean of distribution A corresponds closely with the mode of distribution B? Yes, it is likely that the mean of distribution A corresponds closely with the mode of distribution B.