6.2 histograms

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Good morning!

Schedule: 

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

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)

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

1. Discreet
2. Continuous

Continuous or discrete data?
The temperature in October in India.

1. Discreet
2. Continuous

Continuous or discrete data?
Number of cellphones in this classroom

1. Discreet
2. Continuous

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

Cumulative frequency curve from grouped discrete data

Histograms

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

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

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

Histograms for grouped data

No spaces between bars!

Histograms for grouped data

Histograms for grouped discrete data

Number of eggs	Frequency
1-3	90
4-6	39
7-9	13
10-12	2

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.

Histograms for ungrouped discrete data

Number of eggs	Frequency
0	20
1	30
2	22
3	18
4	15
5	12

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 ?

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. 

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

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

​235​​2​​=0,01

​235​​52​​=0,22

​235​​93​​=0,40

​235​​30​​=0,13

​235​​25​​=0,11

​235​​30​​=0,13

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

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