### Mathematics Class IX

Number Systems
Polynomials
Coordinate Geometry
Lines and Angles
Triangles
Circles
Constructions
Heron’s Formula
Surface Areas and Volumes
Statistics
Probability

# Geographical Representation of Data

As you know a picture is better than thousand words so represent data in an easier way is to represent it graphically. Some of the methods of representing the data graphically are

1. Bar Graph

It is the easiest way to represent the data in the form of rectangular bars so it is called Bar graph.

• The thickness of each bar should be the same.
• The space between in bar should also be same.
• The height of the bar should be according to the numerical data to be represented.

Example

Represent the average monthly rainfall of Nepal for the first six months in the year 2014.

Solution

• On the x-axis mark the name of the months.
• On the y-axis mark the class interval which we have chosen.
• Then mark the average rainfall respective to the name of the month by the vertical bars.
• The bars could be of any width but should be same.
• This is the required bar graph.

2. Histogram

It is like the Bar graph only but it is used in case of a continuous class interval.

• The class intervals are to be taken along an x-axis.
• The height represents the frequencies of the respective class intervals.

Example

Draw the histogram of the following frequency distribution.

Solution

• Mark the daily earnings on the x-axis.
• Mark the no. of stores on the y-axis.
• As the scale is starting from 700 so we will mark the zigzag to show the break.
• Mark the daily earnings through the vertical bars.

3. Frequency Polygon

To draw the frequency polygon

• First, we need to draw a histogram
• Then join the midpoint of the top of the bars a line segment and the figure so obtained is required frequency polygon.
• The midpoint of the first bar is to be joined with the midpoint of the imaginary interval of the x-axis
• The midpoint of the last bar is to be joined with the midpoint of the next interval of the x-axis.

If we need to draw the frequency polygon without drawing the histogram then first we need to calculate the class mark of each interval and these points will make the frequency polygon.

Example

Draw the frequency polygon of a city in which the following weekly observations were made in a study on the cost of living index without histogram.

Step 1: First of all we need to calculate the class mark of each class interval.

Step 2: Take the suitable scale and represent the class marks on the x-axis.

Step 3: Take the suitable scale and represent the frequency distribution on the y-axis.

Step 4: To complete the frequency polygon we will join it with the x-axis before the first class and after the last interval.

Step 5: Now plot the respective points and join to make the frequency polygon.

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