__maths__>__Statistics and Probability__>__Statistics : Analysis of Data__### Bar-graphs : Representation and Reading

Reading a bar-graph of given data is explained with some examples.

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Consider the graph given in figure. What is the representation called?

- the figure does not provide any data
- the figure is a bar-graph representation of a data
- the figure is a bar-graph representation of a data

The answer is "the figure is a bar-graph representation of a data"

The data is represented with horizontal or vertical bars. This representation is spatially laid out for users to easily understand comparative measures like

which one is the largest

which one is the smallest

which ones are comparatively equal.

Consider the data: Number of glasses of water students drink during the school time. Can this data be represented using a bar graph?

- Yes, the number of students in vertical axis and number of glasses in horizontal axis.
- Yes, the number of students in vertical axis and number of glasses in horizontal axis.
- No. The bar graph representation cannot be used for this data.

The answer is "Yes, the number of students in vertical axis and number of glasses in horizontal axis."

Considering the Number of glasses of water students drink during the school time. The bar graph representation is given in the figure. The horizontal axis is the number of glasses and the vertical axis is the number of students. The height of each bar is given for clarity.

A bar of height `11` at position `1` provides information that `11` students had `1` glass of water.

Consider the given bar graph. How many students drank `3` glasses of water?

- `6`
- `6`
- `3`

The answer is "`6`". The height of bar at the position `3` glasses water is `6`.

Consider the given bar graph. This measures the messages sent by a person. The data is number of sentences in a message and the number of messages with the given number of sentences How many messages were sent with `1` sentence?

- `2`
- `2`
- cannot find this info from the bar graph

The answer is "`2`". The height of bar at the position `1` (number of sentences) is `2` number of messages.

Consider the given bar graph. This represents the messages sent by a person. How many number of sentences were there in message of highest frequency?

- `2`
- `2`
- `4`

The answer is "`2`". The message of highest frequency is represented by the tallest bar. For the tallest bar, the number of sentences is `2` (the value on horizontal axis).

Consider the given bar graph. This measures the messages sent by a person. Which two data-values are equal?

- messages with `4` and `5` sentences have the same frequency
- single sentence and `4` sentence messages have the same frequency
- single sentence and `4` sentence messages have the same frequency

The answer is "single sentence and `4` sentence messages have the same frequency".

Reading a bar graph: With the meaning attributed to horizontal axis and vertical axis, the position and height of each bar is read. The objective is to answer any comparative or quantitative questions about the data using the given bar graph.

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