TUTORIAL 01
● TA introductions
TUTORIAL 02
Displaying Data (easy to see patterns in data and get informed about the data collected)
● Tables - easy to see raw numbers for each category
○ Easy to
■ Determine qualitative variables
○ Hard to
■ View changes overtime when comparing tables
■ Absorb info and compare to picture
● Bar Graphs - easy to see raw numbers with visuals
○ Easy to
■ Determine comparisons
■ Absorb information
● Pie Chart - Used as a proportional visual display
○ Easy to
■ See visual representations
■ Wedges represent portion of a whole
○ Hard to
■ See quantitative data
● Example 01: Pie chart of transportation (no numerical values given
○ Bus > Car = Cycle > Walk > Taxi
■ Q. Most common form of travel? ANS. Bus
■ Q. What percentage of people travel by car? ANS. Approx. ¼
■ Q. If 40 people travel by car, how many people took the survey? ANS. Approx. 160 people.
● Example 02: Bar chart on how people get their news
○ Internet (12), Newspaper (10), Radio (12), TV (16)
■ Q. What is the most popular? ANS. TV
■ Q. How many get their news by newspaper? ANS. 10
● Contingency Tables - has two variables, particularly two categorical ones.
○ Marginal Questions - only asks for one variable, not both.
■ Determined by looking at values outside of margins
○ Joint Questions - only asks for two variables, not one
■ Determined by looking at values inside the margins
■ Keyword x “and” y
○ Conditional Questions - fixes on one variable while determining the other
■ Keywords “Out of the x” or “Among the x”
○ Example for Contingency Tables 01
■ Variables.
● Do you drink coffee? Yes or No
, ● What is your sex? Male or Female.
Yes No Total
Male 40 60 100
Female 70 30 100
Total 110 90 200
■ Q. Proportion who drink coffee? ANS. 110/200
■ Q. Proportion who are male? ANS. 100/200
■ Q. Proportion who are male and drink coffee? ANS. 40/200
■ Among women, proportional who drink coffee? ANS.70/100
○ Example for Contingency Tables 02
■ Variables
● Sex? Male or Female
● Opinion? In Favour, No Opinion, Opposed.
In Favour No Opinion Opposed
Male 330 165 55
Female 225 180 45
■ Q. Proportion in favour? ANS. (330+225)/1000
■ Q. Among women, proportion in favour? ANS. 225/(225+180+45)
TUTORIAL 03
Spread IQR:
● Range between 1st and 3rd quartile = Q3 - Q1
● Range - a distance between minimum and maximum
● Boxplot fences
○ Lower fence = Q1 - 1.5*IQR
○ Upper fence = Q3 + 1.5*IQR
● Shape
○ Symmetric - mean = median
○ Skew to right - mean > median
○ Skew to the left - mean < median
Ex. Data 2, 7, 3, 4, 3, 5, 11
1. Sort Data - 2, 3, 3, 4, 5, 7, 11
2. Median - middle value = 4
3. Q1 - median of 1st half of the data = 3
4. Q3 - median of 2nd half of the data = (5+7)/2 = 6
5. IQR = Q3 - Q1 = 6-3 = 3
6. Fences
a. Lower Fence = Q1 - 1.5IQR = 3 - 1.5*3 = -1.5
i. NOTE: If value is negative or very far off, choose the closest number that is in your given data
points.
b. Upper Fences = Q3 - 1.5IQR = 6 + 1.5*3 = 10.5
7. Draw boxplot
● TA introductions
TUTORIAL 02
Displaying Data (easy to see patterns in data and get informed about the data collected)
● Tables - easy to see raw numbers for each category
○ Easy to
■ Determine qualitative variables
○ Hard to
■ View changes overtime when comparing tables
■ Absorb info and compare to picture
● Bar Graphs - easy to see raw numbers with visuals
○ Easy to
■ Determine comparisons
■ Absorb information
● Pie Chart - Used as a proportional visual display
○ Easy to
■ See visual representations
■ Wedges represent portion of a whole
○ Hard to
■ See quantitative data
● Example 01: Pie chart of transportation (no numerical values given
○ Bus > Car = Cycle > Walk > Taxi
■ Q. Most common form of travel? ANS. Bus
■ Q. What percentage of people travel by car? ANS. Approx. ¼
■ Q. If 40 people travel by car, how many people took the survey? ANS. Approx. 160 people.
● Example 02: Bar chart on how people get their news
○ Internet (12), Newspaper (10), Radio (12), TV (16)
■ Q. What is the most popular? ANS. TV
■ Q. How many get their news by newspaper? ANS. 10
● Contingency Tables - has two variables, particularly two categorical ones.
○ Marginal Questions - only asks for one variable, not both.
■ Determined by looking at values outside of margins
○ Joint Questions - only asks for two variables, not one
■ Determined by looking at values inside the margins
■ Keyword x “and” y
○ Conditional Questions - fixes on one variable while determining the other
■ Keywords “Out of the x” or “Among the x”
○ Example for Contingency Tables 01
■ Variables.
● Do you drink coffee? Yes or No
, ● What is your sex? Male or Female.
Yes No Total
Male 40 60 100
Female 70 30 100
Total 110 90 200
■ Q. Proportion who drink coffee? ANS. 110/200
■ Q. Proportion who are male? ANS. 100/200
■ Q. Proportion who are male and drink coffee? ANS. 40/200
■ Among women, proportional who drink coffee? ANS.70/100
○ Example for Contingency Tables 02
■ Variables
● Sex? Male or Female
● Opinion? In Favour, No Opinion, Opposed.
In Favour No Opinion Opposed
Male 330 165 55
Female 225 180 45
■ Q. Proportion in favour? ANS. (330+225)/1000
■ Q. Among women, proportion in favour? ANS. 225/(225+180+45)
TUTORIAL 03
Spread IQR:
● Range between 1st and 3rd quartile = Q3 - Q1
● Range - a distance between minimum and maximum
● Boxplot fences
○ Lower fence = Q1 - 1.5*IQR
○ Upper fence = Q3 + 1.5*IQR
● Shape
○ Symmetric - mean = median
○ Skew to right - mean > median
○ Skew to the left - mean < median
Ex. Data 2, 7, 3, 4, 3, 5, 11
1. Sort Data - 2, 3, 3, 4, 5, 7, 11
2. Median - middle value = 4
3. Q1 - median of 1st half of the data = 3
4. Q3 - median of 2nd half of the data = (5+7)/2 = 6
5. IQR = Q3 - Q1 = 6-3 = 3
6. Fences
a. Lower Fence = Q1 - 1.5IQR = 3 - 1.5*3 = -1.5
i. NOTE: If value is negative or very far off, choose the closest number that is in your given data
points.
b. Upper Fences = Q3 - 1.5IQR = 6 + 1.5*3 = 10.5
7. Draw boxplot
