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

2022
Views:

60

Pages:

4
Author:

Niklas

Exercise 1. A recent survey on Italian young people indicates than 185% of respondents have read more than 3 books over the last six months, 55% of respondents have read less than 3 books and 27% haven't read any book. The results are based on telephone interviews with 1200 people living in Italy, aged 18-34. a. Describe the population of interest; b. Describe the collected sample: c. Describe a parameter of interest; d. Describe the data graphically. a. The population of interest are all the young people that lives in Italy that are between the age of 18 and 34 years old 6. The colected sample are the 1200 people living in Italy age 18 to 34 population C. A parameter of interest, for example, is the proportion of population who have read more than three books over the last six months ol. Since we are dealing with a quantitative discrete variable, the best way to describe the data graphically is the BAR PLOT 660 324 216. ABSOLUTE FREQUENCIES: X3 18%, 1200 size 0.18 0.18 N 0.55==D0.55 0.27 0.27= N 23 55%, 1200 size 0.27%, 1200 size 4200 1200 x 1200 1200-(660+216) = 324 216 X=660 X=324 0 In the y-axis we can have either absolute frequencies or deusity density when w is different ? Exercise 2. Classify the following variables as categorical (nominal/ordinal) or numerical (discrete/continuous): a. Customer satisfaction of Amazon; Categorical ordinal b. Techno subgenres: Categorical nominal c. National identification number: Numerical discrete d. Number of students in a class: Numerical discrete e. Bank account balance: Numerical continuous f. Average number of lottery tickets sold: Numerical continuous Exercise 3. The table below shows the frequencies of a categorical variable with three categories: Category A B Thi 5 fi 0.1 Pi 0.1 13 0.26 0.36 C 32 0.64 1 a. Complete the table; 50 b. Construct a bar chart; c. Construct a pie chart. 5 5 a. fifa 0.1=x= =5.10 = 50 X= 1 N N N= N,+N2+N350=5+13+33=50-5-13-32 f2==0.26 N 50 fo3:32=0.64 N 50 b. 30+ 20 3 abs freg 10 5 1 2 c. augle 360 fi 1 augle 36°, 2 augle = 93.6°, 3 augle = 230.4° 1 2 3 7 Exercise 4. The number of goals scored by a team in 20 games are given below. 4 0 3 1 0 1 2 3 1 2 2 1 0 1 3 5 0 1 30 Using 3 class intervals with the lowest starting at 0: a. Set up a frequency distribution; b. Construct a cumulative frequency distribution; c. Draw a histogram; d. Compute the relative frequencies and plot them: c. Compute the cumulative relative frequencies and plot them. Exercise 5. The values for a set of data vary from 11 to 59. Using 6 class intervals: a. Compute the class-interval width: b. Indicate the class boundaries: c. Compute the six class midpoints. a. To compute the class-interval width we choose first of all the maximum aud the minimum points, they have to larger than the last point of the last interval and smaller thau the first point of the first interval. In this case we raudomly choose 65 as Rmax and 5 as Rmin. width = Range of the entire data number of classes Rmax - Rmin 65-5 = 10 6 #intervals I want to make b. If the width of the intervals is 10, the class boundaries are: [5,15), [15,25), [25,35), [35,45), [45,55), [55,65) The mid point are calculated as Xmax+ Xmin over 2 15+5 X210 X= = 40 45+35 2 55+45 25+15 2 -20 X= 2 = 50 35+25 2 = 30 X 65+55 2 -60