# 6.2 histograms

Good morning!
Schedule:
• Learning goals
• Homework questions?
• Practice with cumulative frequency curves (Standard)
• Histograms (Extended)
• Continuous data and discrete data
• Homework
1 / 22
Slide 1: Tekstslide
WiskundeMiddelbare schoolvwoLeerjaar 3

In deze les zitten 22 slides, met interactieve quizzen en tekstslides.

## Onderdelen in deze les

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
• There are spaces between the bars

Histogram:
• ∙Quantitative data
• ∙May or may not have equal width
• Area of bar represent frequency
• No spaces between the bars

Histogram

#### Slide 10 -Tekstslide

Histogram
Bar chart:
- qualitative
- spaces between bars
Histogram:
- quantitative
- No spaces between bars
Histogram:
- quantitative
- No spaces between bars
Neither:
- quantitative
- Spaces between bars
- Percentage on y-axis

#### Slide 11 -Tekstslide

Histograms for grouped data
No spaces between bars!

#### Slide 12 -Tekstslide

Histograms for grouped data

#### Slide 13 -Tekstslide

Histograms for grouped discrete data
Number of eggs
Frequency
1-3
90
4-6
39
7-9
13
10-12
2

#### Slide 14 -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 15 -Tekstslide

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

#### Slide 16 -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 17 -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 18 -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 19 -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 20 -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 21 -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