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

2022
Views:

197

Pages:

3
Author:

Niklas

Exercise 1: Title: "The following frequency distributions represent the age distribution of a sample of 110 people covered by health insurance. Find the mean and the median." Table: A frequency distribution table with the following columns: CV: Class Value Age: Age Range Frequency (n): Number of people in the age range Calculations: Mean: The mean age is calculated as 45.4. Median: The median age is found to be 55.5, which is contained in the second interval. Exercise 2: Title: "Find an estimate of the variance and standard deviation of the following data for the marks obtained in a test by 88 students." Table: A frequency distribution table with the following columns: Marks (x): Marks Range Frequency (n): Number of students with the corresponding marks Calculations: Mean: The mean marks are calculated as 28.5. Variance: The variance is calculated as 138.7. Standard Deviation: The standard deviation is calculated as 11.8. Exercise 3: Title: "Suppose that the scores to a given test of two groups of students are..." Data: The test scores for students of class A and class B are provided. Parts: a. Compute the means and the variances of the two groups. b. Compute the global mean and the total variance. c. Quantify the difference among the two groups by using appropriate measures and interpret the results. Calculations: Means and Variances: The means and variances for both groups A and B are calculated. Global Mean and Total Variance: The global mean and total variance are computed. Difference Between Groups: The difference between the groups is quantified using the variance explained by the groups. Exercise 4: Title: "The plot below represents the cdf of a set of 10 observations (x-axis: 1,2,3,4,5,6,7, y-axis: 0,0.179, 0.339, 0.482, 0.643, 0.786, 0.911, 1)." Plot: A cumulative distribution function (CDF) plot showing the distribution of the 10 observations. Parts: a. What is the first quartile? b. What is the mean? Table: A table summarizing the data, including the frequency (f), cumulative frequency (F), and product of x and f. Calculations: First Quartile: The first quartile is found to be 2. Mean: The mean is calculated as 3.66.