12:55 7 Assignment2_Coffeedataset AD Q . . . fx B C D E F G H StudentID DrinkCoffee Age Gender City Yes 17 Female Vancouver Yes 19 Female Richmond Yes 19 Female Richmond 5 Yes 20 Female Vancouver 6 Yes 26 Male Vancouver Yes 23 Female Vancouver 8 Yes 31 Female Vancouver 8 Yes 19 Female Richmond 10 9 Yes 20 Female Vancouver 11 10 Yes 23 Male North Vancouver 12 11 No 19 Male Burnaby 13 12 Yes 19 Female Vancouver 14 13 Yes 19 Male Burnaby 15 14 Yes 20 Female Surrey 16 15 Yes 21 Male Richmond 17 16 Yes 18 Female Langley 18 17 Yes 26 Female Richmond 19 18 Yes 35 fer not to ans Vancouver 20 19 Yes 22 Male New Westminster 21 20 No 19 Female Richmond 22 21 Yes 18 Female Surrey 23 22 Yes 19 Male Vancouver 24 23 Yes 21 Female Vancouver 25 24 Yes 18 fer not to ans Vancouver 26 25 No 21 Female Vancouver 27 26 Yes 21 Female Abbotsford 28 27 No 18 Female Burnaby 29 28 Yes 19 Female Surrey 30 29 Yes 20 Female Vancouver 31 30 No 18 Female Burnaby 32 31 No 17 Female Vancouver 33 32 Yes 25 Female Surrey 34 33 Yes 27 Male Vancouver 35 34 Yes 20 Male Richmond 36 35 Yes 18 Female Vancouver 37 36 Yes 21 Female Richmond 38 37 Yes 23 Male Surrey 39 38 Yes 19 Female Richmond 40 39 No 19 Female Richmond 41 40 Yes 24 Female Surrey 42 41 Yes 20 Female Surrey 43 42 Yes 18 Female Langley 44 43 Yes 24 Female Vancouver 45 44 No 18 Female New Westminster 46 45 No 18 Female Surrey 47 46 No 18 Female Surrey 48 47 Yes 18 Female Vancouver 49 48 No 21 Male Richmond 50 49 No 18 Female Vancouver 51 50 Yes 17 Male Vancouver 52 51 Yes 17 Male Vancouver 53 52 Yes 18 Female Richmond 54 53 No 22 Male Vancouver 55 54 Yes 23 Female Vancouver 56 55 Yes 19 Female Maple Ridge 57 56 Yes 18 Female Vancouve 58 57 Yes 21 Female Richmond 59 58 No 19 Female Vancouver 60 59 Yes 18 Male Richmond 61 60 Yes 18 Male Richmond 62 61 No 18 Female Vancouver 63 62 No 25 Female Vancouver 64 63 Yes 21 Male Richmond 65 64 Yes 21 Female Vancouver 66 65 Yes 20 Female Surrey 57 . . .b} Obtain the S-number summary (report the actual values and indicate what they are] and a boxplot of the variable 'age'. [2 marks] c) Obtain a numerical summary of one measure of center and one measure of variation for the variable 'age'. Note that these measures should be appropriately chose for this variable and based on the distribution of this variable (Hint: think about the shape of the variable 'age' that you identified in part al). [2 marks] d] Interpret the distribution of the variable 'age' based on your answers a) - c). (Hint: make sure you comment on shape, center, spread and outliers (if any!)). [4 marks] 3. [6 marks] The objective of this exercise is to investigate the relationship between one categorical variable and one quantitative variable (this is an example of a bivariate analysis). In particular, we want to compare the distributions of students' age for those who said 'yes' to drinking coffee with students' age for those students who said 'no' to drinking coffee. a) Obtain side-by-side box and whisker plots of age for drinking coffee. [2 marks] b] Use the graphical display in part a to compare the distributions of age for the two groups of drinking coffee. Make sure you comment and compare shape, center, spread and outliers (if any!) between the two boxplots. [4 marks] 4. [4 marks] It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, minutes of activity varied according to the N873, 67) distribution. Minutes of activity for lean people had the N(526, 107) distribution. Within what limits do the active minutes for about 95% of the people in each group fall? Use the 68-95-993! rule. 5. [6 marks] The return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percent of the beginnlng price. The distribution of the annual percentage returns for all stocks listed on the S&P 500 from 1928 to 2018 (91 years} is normal with an average return of 11.36%, with a standard deviation of 19.58%. a) What is the proportion of years with returns greater than 0% annual return? [2 marks] b] What is the proportion of years with returns between 40% and ~20% annual return? [2 marks] c) Above what annual percentage return are the top 10% of the years? [2 marks] STATISTICS 1 123 Homework Assignment #2 Using Statgraphioa to Summarize Data & Normal Distributions TOTAL = 43 MARKS Due Date: Februa 6, 2022 For this assignment, you will be using Excel to conduct both univarlate and bivariate data analyses. Questions 1I 2 and 3 must be done in MS Excel software. In this statistical investigation, data was collected on 65 Langara students and their interest in drinking coffee was investigated. The following 4 variables were collected on these students: age (in years], gender, city {where a student lives), whether or not they drink coffee. This dataset is available in 'MS Excel' format {lename: Assign ment2_CoffeeDataset.xlsx] and it can be accessed from Conte nt/Assignments mod ule on our course website. The structure of this dataset is su mmarized as follows: StudentlD Age [in years] Gend er DrinkCoffee 1. [15 marks] The objective of this exercise is to summarize and describe data for a single categorical variable [this is an example of a univariate analysis of a categorical variable]. a] Obtain a numerical summary [report both frequency and percentage] for each of the categorical variables in this dataset (hint: gender, city, and drinkcoffee]. [6 marks] b] Obtain a barchart or a piechart (Le. graphical summary] for each of the categorical variables in this dataset. Make sure each of your graphical summaries has a title and the axes of your graphs are clearly labeled. [6 marks] c] Provide an interpretation for each of these three variables based on your results in parts a] and b]. In other words, what do the numerical and graphical summaries tell you about the distributions of each of these variables? [3 marks] 2. [12 marks] The objective of this question is to summarize and describe data for a single quantitative variable [this is an example of univariate analysis of a quantitative variable]. a] Obtain a histogram {showing frequency on the y-axis] for the variable 'age'. Make sure your histogram has a title and the axes are clearly labeled. Make sure you do not over-summarize or under- summarize the histogram use an appropriate number of bins (i.e. classes]. [4 marks]