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# Bar Graphs

Suppose your class-teacher wants to show the class the comparison of the marks of students in all subjects. Is it possible for her to remember the marks of each and every student in all subjects? No! Also, she doesn’t have the time to compare the marks of every student. Moreover, how can she make the comparison interesting? She can graphically show the comparison. How? She can use Bar graphs, histograms, pie graphs, line graph etc. to do the comparison.  Let us start what all these are.

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It is the simplest one among the graphs. A bar graph is a graphical representation of the data in the form of rectangular bars or columns of equal width. It is the simplest representation of data.

### Properties of Bar Graphs

• Each bar or column in a bar graph is of equal width.
• All bars have a common base.
• The height of the bar corresponds to the value of the data.
• The distance between each bar is the same.

### Construction of a Bar Graph

1. Draw two perpendicular lines intersecting each other at a point O. The vertical line is the y-axis and the horizontal is the x-axis.
2. Choose a suitable scale to determine the height of each bar.
3. On the horizontal line, draw the bars at equal distance with corresponding heights.
4. The space between the bars should be equal.

## Types of Bar Graphs

A bar graph can be either vertical or horizontal depending upon the choice of the axis as the base. Let us take an example for bar graph showing the comparison of marks of a student in all subjects out of 100 marks. With the bar graph, we can also compare the marks of students in each subject other than the marks of one student in every subject. Also, we can draw the bar graph for every student in all subjects.

## Histogram

A histogram is similar to a bar graph except for the fact that there is no gap between the rectangular bars. The rectangular bars show the area proportional to the frequency of a variable and the width of the bars represents the class width or class interval.

Frequency means the number of times a variable is occurring or is present. It is an area graph. The heights of the rectangles are proportional to the corresponding frequencies of similar classes.

### Properties of Histogram

1. Each bar or column in a bar graph is of equal width and corresponds to the equal class interval.
2. All bars have a common base.
3. The height of the bar corresponds to the frequency of the data.

### Construction of a Histogram

1. Draw two perpendicular lines intersecting each other at a point O. The vertical line is the y-axis and the horizontal is the x-axis.
2. Choose a suitable scale for both the axes to determine the height and width of each bar.
3. On the horizontal line, draw the bars with corresponding heights.

Let us take an example for bar graph showing the comparison of marks of 20 students in Mathematics out of 100 marks. Let us find out the number of students in the various ranges (categories) of the marks. ## Line Graph

A line graph is a type of a chart or graph which shows information when a series of data is joined by a line. It shows the changes in the data over a period of time.

### Properties of a line graph

• It consists of Vertical and Horizontal scales. These scales may or may not be uniform.
• Data point corresponds to the change over a period of time.
• The line joining these data points shows the trend of change.
• The line graph showing the number of cars passing through a particular street over a period of time:

## Solved Example for You

Question 1.  From the given line graph answer the following questions

### 1. What was the speed of the car at 1:00 PM?
2. Find the difference in the speed of the car for the time 10 AM and 11 AM?
3. What are the maximum and the minimum speed of the car?

Answer : From the line graph,

1. The speed of the car is 55 km/h.
2. The difference in speed of the car = (72 − 45) km/h = 27 km/h.
3. The maximum speed = 75 km/h and the minimum speed = 39 km/h.

Question 2: What are the bar graphs?

Answer: Bar graphs are one of the simplest one amongst the graphs. It is a graphical representation of the data in the shape of rectangular bars or columns of equal width. Moreover, it also refers to being the simplest representation of data.

Question 3: List the properties of the bar graphs?

Answer: The properties of bar graphs are that firstly, each bar or column of the bar graph has equal width. Further, all the bars have a common base. Similarly, the height of the bar is corresponding to the value of the data. Finally, in bar graphs, the distance between each of the bars is the same.

Question 4: What is a histogram?

Answer: A histogram refers to a bar graph with an exception that it does not consist of a gap between the rectangular bars. Moreover, the rectangular bars denote the area proportional to the frequency of a variable plus the width of the bars denotes the class width or class interval.

Question 5: What is the line graph?

Answer:A line graph refers to a kind of chart or graph that shows us information when a series of data is joined by a line. Similarly, it represents the changes in the data over a phase of time.

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