6.1 Comparing data & outliers

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Good morning!

Schedule: 

• Learning goals
• Problem solving questions
• Review exercise
• Outliers
• Do some research!

Learning goals

At the end of these this lesson I can:

• Find the five point summary from a set of data 
• Construct a boxplot from a set of data
• Find outliers from a set of data

Problem solving

What strategies did we find last time? 

- 

Problem solving

What strategies did we find last time? 

- Trial and Error

- Divide problem in smaller problems/steps

- Work backwards (start with the answer)

​3​​1​​m=​5​​1​​m+3−1

​15​​5​​m=​15​​3​​m+3−1

​15​​2​​m=2

2m=30

m=15

Problem solving

Problem solving strategies:

- Trial and Error

- Divide problem in smaller problems/steps

- Work backwards (start with the answer)

- Realize the problem (literally DO the problem)

- Organize your information differently 

- Use algebraic methods

Review exercise

Key: 1 | 5 | 3 means a student from class 1 got a score of 51 and a student from class 2 got a score of 53

1. Calculate the median and range for class 1 and class 2. 

2. Calculate the IQR for class 1 an class 2 

Review exercise

Key: 1 | 5 | 3 means a student from class 1 got a score of 51 and a student from class 2 got a score of 53

n = 28 

Middle values = 14^th and 15^th

Median =

Range =  

​2​​70+71​​=70.5

95−45=50

Class 1

Review exercise

Key: 1 | 5 | 3 means a student from class 1 got a score of 51 and a student from class 2 got a score of 53

n = 28 

Middle values = 14^th and 15^th

Median =

Range =  

​2​​65+66​​=65.5

91−41=50

Class 2

Review exercise

Key: 1 | 5 | 3 means a student from class 1 got a score of 51 and a student from class 2 got a score of 53

n = 28 

Q₂ = median =  70.5

Q1 =

Q3 =

IQR = Q3 - Q1 = 82.5 - 62 = 20.5

Class 1

|

​2​​(61+63)​​=62

​2​​(82+83)​​=82.5

Review exercise

Key: 1 | 5 | 3 means a student from class 1 got a score of 51 and a student from class 2 got a score of 53

n = 28 

Q₂ = median =  65.5

Q1 =

Q3 =

IQR = Q3 - Q1 = 75 - 55 = 20

Class 2

|

​2​​(55+55)​​=55

​2​​(74+76)​​=75

Outliers

You do not count outliers in the 5 point summary (as Min or Max) !!

Outliers

 <    Q₁ - IQR x 1.5      Q₁       Q₂       Q₃      Q₃ +  IQR x 1.5   >

Outliers

Outliers

Outliers

17, 18, 20, 20, 21, 22, 23, 23, 24, 24, 24, 24, 25, 26, 26, 27, 27, 30, 46

                                      

                                            Q₁ = 21,  Q₂ = 24, Q₃ = 26  

                                           IQR = Q₃ - Q₁ = 26 - 21 = 5

                               Calculate if there are any outliers

Outliers

17, 18, 20, 20, 21, 22, 23, 23, 24, 24, 24, 24, 25, 26, 26, 27, 27, 30, 46

                                       Q₁ = 21,  Q₂ = 24, Q₃ = 26     IQR = 5

Minimum = Q1 - 1.5 x IQR = 21 - 1.5 x 5 = 13.5

There are NO values smaller than 13.5

Maximum = Q3 + 1.5 x IQR = 26 + 1.5 x 5 = 33.5

There is one value larger than 33.5                            

                                   

                            

49 is an outlier

Outliers

17, 18, 20, 20, 21, 22, 23, 23, 24, 24, 24, 24, 25, 26, 26, 27, 27, 30, 46

                                       Q₁ = 21,  Q₂ = 24, Q₃ = 26     IQR = 5

Minimum = Q1 - 1.5 x IQR = 21 - 1.5 x 5 = 13.5

         

                                   

                            

Outliers

17, 18, 20, 20, 21, 22, 23, 23, 24, 24, 24, 24, 25, 26, 26, 27, 27, 30, 46

                                       Q₁ = 21,  Q₂ = 24, Q₃ = 26     IQR = 5

Minimum = Q1 - 1.5 x IQR = 21 - 1.5 x 5 = 13.5

There are NO values smaller than 13.5

        

                                   

                            

Outliers

17, 18, 20, 20, 21, 22, 23, 23, 24, 24, 24, 24, 25, 26, 26, 27, 27, 30, 46

                                       Q₁ = 21,  Q₂ = 24, Q₃ = 26     IQR = 5

Minimum = Q1 - 1.5 x IQR = 21 - 1.5 x 5 = 13.5

There are NO values smaller than 13.5

Maximum = Q3 + 1.5 x IQR = 26 + 1.5 x 5 = 33.5                 

                                   

                            

Outliers

17, 18, 20, 20, 21, 22, 23, 23, 24, 24, 24, 24, 25, 26, 26, 27, 27, 30, 46

                                       Q₁ = 21,  Q₂ = 24, Q₃ = 26     IQR = 5

Minimum = Q1 - 1.5 x IQR = 21 - 1.5 x 5 = 13.5

There are NO values smaller than 13.5

Maximum = Q3 + 1.5 x IQR = 26 + 1.5 x 5 = 33.5

There is one value larger than 33.5                            

                                   

                            

46 is an outlier

Take out your diaries 

Homework for Monday 15-3-2021:

                              Practice 7 on p. 321-322

Social media research 

Go to ManageBac and fill in the questionnaire. 

You can find average screen time per app (if you don't have this option or you can give a good estimate, please do that!) 

- Android: Settings > Digital Wellbeing and parental controls > Dashboard (click the Numbers next to Apps) > Click the app > Click weekly (go back one week to find your average screen time from last week) 

- Iphone: Settings > Screen Timer > Show all activity > Click app to find the average

Let's do some research!

1. Go to Manageback and find the data from your survey's. 

2. Choose one of the 3 categories to do your research on: 

• Time spend on Physics homework 
• Time spend on Math homework
• Time spend on English homework

3. Draw up a back-to-back stem-and-leaf diagram of your chosen data dividing male and female data, and a boxplot for both male and female data. 

4. Calculate the five point summary and IQR for both male and female data.

5. Calculate whether there are any outliers in the data.