Using The Birdwatch Project to promote Maths and ICT learning

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What skills?

Types of graphs & charts – test

Answers

1 Histogram 7 Carroll Diagram

2 Pictogram 8 Block graph

3 Table 9 Bar line graph

4 Line graph 10 Venn diagram

5 Tally chart 11 Bar chart

6 Pie chart 12 Frequency table

Click on each term for a definition.

You will see that the same data can be represented in different ways. This is often a matter of personal choice, choosing a method of display that appears to demonstrate a particular feature of the data well.

Questions: What is a bar chart? What is a bar line graph / chart?

Answer: A bar chart, which can also be called a bar graph, is used for representing statistical information.

The lengths of the bars represent the frequencies and all the bars are of equal width. Technically, the bars can be horizontal or vertical. For discrete data, the bars should not be touching.

Bar chart / Bar graph Bar line graph / Bar line chart

A bar line graph is very similar, but with the bars reduced in width to become lines. Note the different ways of labelling the horizontal axis.

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Question: What is a histogram?

Answer: A histogram, like a bar chart, uses rectangles to represent frequency.

The bars in a histogram should touch each other. They don’t all have to be the same width – the bar widths are proportional to the intervals used for the data.

The other important difference with histograms is that the area of each bar represents the frequency (not the height of the bar as in bar charts).

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Question: What is a Carroll Diagram?

Answer: This is a sorting diagram, named after Lewis Carroll, the author and mathematician.

It is most often used to sort items with two attributes, like the example below. The sorting criteria should always be in the form ‘attribute’ or ‘not attribute’.

Here the integers 1 – 20 are sorted according to the attributes Prime or Not Prime, Odd or Not Odd.

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Prime Not Prime

Odd 3, 5, 7, 11, 13, 17, 19

1, 9, 15

Not Odd

2 4, 6, 8, 10, 12, 14, 16, 18, 20

Question: What is a Venn diagram?

Answer: This is a sorting diagram, named after the Yorkshire-born mathematician John Venn.The example below sorts the integers 1 – 20 according to whether

they are odd and/or prime or neither (as with the Carroll Diagram example)

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OddPrime

3, 5, 7, 11, 13, 17, 19

2 1

9

15

4 68 10 12

14

16 18 20

Answercontinued

Question: What is a Venn diagram?

Answer (continued): The diagram comprises a number of circles or ellipses. The content of a circle has a particular attribute, items without the attribute are outside that circle.

With only two attributes, the diagram has the same four categories as a corresponding Carroll Diagram. When additional attributes are needed, the Venn Diagram is generally simpler to draw and use. Other examples of Venn Diagrams where more than two attributes are used include:

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Question: What is a pie chart?

Answer: also called a Pie diagram, presents data in proportional parts of a whole similar to slices of a pie.

In the example below, the frequency for each of the children’s pets in a class is used to calculate the angles of the pie slices. There are 30 children in the class, so the angle is given by:

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Pets Frequency Pie chartangle

Dog 5 60°

Cat 7 84°

Fish 3 36°

Reptile 4 48°

Rabbit 2 24°

none 9 108°

Total 30 360°

Frequency

Total

X 360°, so for Cat, the angle is 7/30 x 360° = 84°

Question: What is a table? What is a frequency table? What is a tally chart?

Answer: A table can be used to record data, often as it is collected. The example below is a frequency table because it records the frequencies of events/outcomes etc. The centre column shows the tally marks, used to help with the count – so this is also a tally chart.

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Pets Tally Frequency

Dog 1111 5

Cat 1111 11 7

Fish 111 3

Reptile 1111 4

Rabbit 11 2

none 1111 1111 9

Total 30

Question: What is a block graph?

Answer: This is a graph made up of blocks, often produced by children using actual blocks. In the example below, each block represents one unit but each could be used to represent a higher number provided all the blocks represent the same number of units.

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Pets Freq.

Dog 5

Cat 7

Fish 3

Reptile

4

Rabbit 2

none 9

Total 30

Pets

Fre

quen

cy10

9

8

7

6

5

4

3

2

1

Dog

cat fish reptile rabbit none

Question: What is a line graph?

Answer: This type of graph is created by joining the known plotted points by straight lines. Technically, the lines are not part of the graph; the lines merely indicate trends.

Here is an example of a line graph.

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May 12

June 12

July 14

Aug. 11

Sept. 9

Hours of sunshine

xxx

xx

Question: What is a pictogram?

Answer: a pictogram represents the frequencies using pictures, symbols or icons.

One icon can represent a frequency of 1 or a higher quantity, as indicated in the key, and fractions of the icon can be used to represent smaller quantities.

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