6.2 Cumulative frequency curves (and histograms)

Good morning!
Schedule: 
  • Learning goals 
  • Homework questions? 
  • Practice with cumulative frequency curves (Standard)
  • Histograms (Extended)
  • Continuous data and discrete data
  • Homework 
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Slide 1: Tekstslide
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In deze les zitten 18 slides, met interactieve quizzen en tekstslides.

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Good morning!
Schedule: 
  • Learning goals 
  • Homework questions? 
  • Practice with cumulative frequency curves (Standard)
  • Histograms (Extended)
  • Continuous data and discrete data
  • Homework 

Slide 1 - Tekstslide

Learning goals 
At the end of this lessons I can:
  • Represent data in a cumulative frequency curve
  • Draw a cumulative frequency curve for both continuous and discrete data. 
  • Name the differences between bar charts and histograms (Extended)
  • Describe the data distribution from a histogram (Extended)
  • Draw both frequency histograms and relative frequency histograms (Extended)

Slide 2 - Tekstslide

Continuous or discrete data?
Number of people wearing yellow t-shirts
A
Discreet
B
Continuous

Slide 3 - Quizvraag

Continuous or discrete data?
The temperature in October in India.
A
Discreet
B
Continuous

Slide 4 - Quizvraag

Continuous or discrete data?
Number of cellphones in this classroom
A
Discreet
B
Continuous

Slide 5 - Quizvraag

Continuous grouped data and discrete grouped data 
Continuous grouped data: 
Plot the cumulative frequencies against the upper class boundaries 
Discrete grouped data: 
Plot the cumulative frequencies against the halfway point between two classes

Slide 6 - Tekstslide

Cumulative frequency curve from grouped discrete data

Slide 7 - Tekstslide

Histograms
What are the differences between a bar chart and a histogram?

Slide 8 - Tekstslide

Histograms
Bar chart: 
  • ∙Qualitative data
  • ∙Equal Width
  • ∙Height of bar represent frequency

Histogram: 
  • ∙Quantitative data
  • ∙May or may not have equal width
  • ∙Area of bar represent frequency


Slide 9 - Tekstslide

Histogram

Slide 10 - Tekstslide

Histograms for ungrouped discrete data
Number of eggs
Frequency
0
20
1
30
2
22
3
18
4
15
5
12

Slide 11 - Tekstslide

Histograms for grouped discrete data
Number of eggs
Frequency
1-3
90
4-6
39
7-9
13
10-12
2
Plot from the point halfway between the upper boundary of one class and the lower boundary of the next class. 
To make sure all the bars are the same width we start the first bar in this graph at 0.5.

Slide 12 - Tekstslide

Distribution in histograms
When describing the distribution of a histogram make sure to mention: 
- The center: Median class and/or modal class 
- The spread: The range
- The outliers: Extreme data values that don't fit in
- The shape: Unimodal, Bimodal or Multimodal ?

Slide 13 - Tekstslide

Distribution in histograms
When describing the distribution of a histogram make sure to mention: 
- The center: 29th value lies in the class 
60 ≤ x < 70. This is also the modal class. 
- The spread: There is a wide spread in fish length from 20 cm to 120 cm. 
- The outliers: There are no outliers. 
- The shape: Bimodal, the histogram has two peaks

Slide 14 - Tekstslide

Relative frequency histograms
Relative frequency is the proportion/percentage of the data set for a class. 

Relative frequency = 
n(ClassFrequency)
Length, x (cm)
Frequency
Relative frequency
10 < x ≤ 20 
2
20 < x ≤ 30
52
30 < x ≤ 40
93
40 < x ≤ 50
30
50 < x ≤ 60
25
60 < x ≤ 70
33
n = 235 
Lengths of fish caught in Au Sable river

Slide 15 - Tekstslide

Relative frequency histograms
When rounding the relative frequency, make sure it adds up to 1 (or 100%)!!!

Length, x (cm)
Frequency
Relative frequency
10 < x ≤ 20 
2
20 < x ≤ 30
52
30 < x ≤ 40
93
40 < x ≤ 50
30
50 < x ≤ 60
25
60 < x ≤ 70
30
n = 232 
Lengths of fish caught in Au Sable river
2352=0,01
23552=0,22
23593=0,40
23530=0,13
23525=0,11
23530=0,13

Slide 16 - Tekstslide

Frequency histogram
Relative frequency histogram
0    10   20   30   40   50   60   70 
                Fish length (cm)
0    10   20   30   40   50   60   70 
                     Fish length (cm)
150

130



110

90



50 

40

30

20

10


30

10



70

50


Slide 17 - Tekstslide

Relative frequency histogram vs. frequency histogram
- The overall shapes of the histograms are the same
- Relative frequency histograms show the distribution of proportion or percentages of values.
- Frequency histograms show the distribution of the actual values. 

Relative frequency histograms give a graphical image of  a probability distribution

Slide 18 - Tekstslide