True or False? A histogram is used to show the frequency distribution of discrete data.

False. A histogram is used to show the frequency distribution of continuous data.

True or False? A histogram is the same as a bar chart but without the gaps between the bars.

False. A histogram is not the same as a bar chart . A histogram uses frequency density , whereas a bar chart uses frequency.

True or False? The height of a bar in a histogram is equal to the frequency of that class.

False. The height of a bar in a histogram is not equal to the frequency of that class. The height is equal to the frequency density .

True or False? The area of a bar in a histogram is proportional to its frequency .

True. The area of a bar in a histogram is proportional to its frequency . In most cases the area is equal to the frequency.

How can you find the frequency of a part of a class interval from a histogram?

To estimate the frequency of part of a class interval within a histogram: Find the area of the bar for the part of the interval required.

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Histograms (Cambridge (CIE) IGCSE Maths)

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FrontFrequency Density
State the formula for frequency density.

Speed, s (km/h)	Frequency	.........	.........
$20 \leq s < 40$	5
$40 \leq s < 50$	15

Speed, s (km/h)	Frequency	Class width	Frequency Density
$20 \leq s < 40$	5	20	0.25
$40 \leq s < 50$	15	10	1.5

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Cards in this collection (9)

State the formula for frequency density.
The formula for frequency density is:
$frequency density = \frac{frequency}{class width}$ .
When calculating frequency densities, given a table with a first column for the class intervals and a second column for the frequencies, it is useful to add two more columns to the table.
What information should these columns be used for?
Speed, s (km/h)
Frequency
.........
.........
$20 \leq s < 40$
5
$40 \leq s < 50$
15
When calculating frequency densities, given a table with a first column for the class intervals and a second column for the frequencies, two extra two columns should be added for class width and frequency density.
Speed, s (km/h)
Frequency
Class width
Frequency Density
$20 \leq s < 40$
5
20
0.25
$40 \leq s < 50$
15
10
1.5
True or False?
A histogram is used to show the frequency distribution of discrete data.
False.
A histogram is used to show the frequency distribution of continuous data.
True or False?
A histogram is the same as a bar chart but without the gaps between the bars.
False.
A histogram is not the same as a bar chart.
A histogram uses frequency density, whereas a bar chart uses frequency.
What type of statistical diagram is shown below.
The statistical diagram shown is a histogram.
True or False?
The height of a bar in a histogram is equal to the frequency of that class.
False.
The height of a bar in a histogram is not equal to the frequency of that class.
The height is equal to the frequency density.
True or False?
The area of a bar in a histogram is proportional to its frequency.
True.
The area of a bar in a histogram is proportional to its frequency.
In most cases the area is equal to the frequency.
How can you find the frequency of a group from a histogram?
The frequency of a histogram is proportional to the area of the bar.
Therefore, in order to find the frequency for a particular bar, you can find its area by multiplying the height (frequency density) by the width of the bar (class width).
$frequency = frequency density \times class width$
How can you find the frequency of a part of a class interval from a histogram?
To estimate the frequency of part of a class interval within a histogram:
- Find the area of the bar for the part of the interval required.

Speed, s (km/h)	Frequency	.........	.........
$20 \leq s < 40$	5
$40 \leq s < 50$	15

Speed, s (km/h)	Frequency	Class width	Frequency Density
$20 \leq s < 40$	5	20	0.25
$40 \leq s < 50$	15	10	1.5

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