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Graphical Representation of Data - Statistics, Class 9, Mathematics | Extra Documents & Tests for Class 9 PDF Download

GRAPHICAL REPRESENTATION OF STATISTICAL DATA
The tabular representation of data is an ideal way of presenting them in a systematic manner. When these numerical figures are represented pictorially or graphically, they become more noticeable and easily intelligible, leaving a more lasting effect on the mind of the observer. With the help of these pictures or graphs, data can be compared easily.

There are various types of graphs. In this chapter, we shall be dealing with the following graphs:
1. Bar Graphs
2. Histogram
3. Frequency Polygon

BAR GRAPH (OR COLUMN GRAPH OR BAR CHART)
A bar graph is a pictorial representation of numerical data in the form of rectangles (or bars) of equal width and varying heights.
These rectangles are drawn either vertically or horizontally.
The height of a bar represents the frequency of the corresponding observation.
The gap between two bars is kept the same.


Ex.7 The following table shows the number of students participating in various games in a school.
Class IX, Mathematics, NCERT, CBSE, Important, PDF, Download, Textbook, Statistics

Draw a bar graph to represent the above data.

Sol. Take the games along x-axis and the number of students along Y-axis.

Class IX, Mathematics, NCERT, CBSE, Important, PDF, Download, Textbook, Statistics
Along y-axis, take the scale 1 cm = 6 students. The bar-graph may, thus, be drawn as shown alongside.


Ex.8 Given below are data showing number of students of a school using different modes of travel to school.
Class IX, Mathematics, NCERT, CBSE, Important, PDF, Download, Textbook, Statistics

Draw a bar graph to represent the above data.

Sol. Take the mode along x-axis and the number of students along y-axis.
Scale : Along y-axis, take 1 cm = 40 students.
The bars of equal width and proportionate heights with same gap between the two consecutive bars, may be drawn as shown below.
Shading for boys and girls may be done as under :

Class IX, Mathematics, NCERT, CBSE, Important, PDF, Download, Textbook, Statistics

HISTOGRAM
A histogram is a graphical representation of a frequency distribution in an exclusive form in the form of rectangles with class intervals as bases and the corresponding frequencies as heights, there being no gap between any two successive rectangles.

METHOD OF DRAWING A HISTOGRAM

Step 1 : If the given frequency distribution is in inclusive form, convert it into an exclusive form.

Step 2 : Taking suitable scales, mark the class-intervals along x-axis and frequencies along y-axis.
Note that the scales chosen for both the axes need not be the same.

Step 3 : Construct rectangles with class-intervals as bases and the corresponding frequencies as heights.

Ex.9 Draw a histogram to represent the following data :
Class IX, Mathematics, NCERT, CBSE, Important, PDF, Download, Textbook, Statistics

Sol. Draw rectangles with bases 30 – 36, 36 – 42, 42 – 48, 48 – 54 and 54 – 60 and heights 15, 25, 20,
30 and 10 respectively.

Class IX, Mathematics, NCERT, CBSE, Important, PDF, Download, Textbook, Statistics
Note : Since the scale on x-axis starts at 30, we make a kink ( ) in the beginning.

 

Ex.10 Draw a histogram for the following data :
Class IX, Mathematics, NCERT, CBSE, Important, PDF, Download, Textbook, Statistics

Sol. The given table is in inclusive-form. So, we first convert it into an exclusive form, as given below.
Class IX, Mathematics, NCERT, CBSE, Important, PDF, Download, Textbook, Statistics
Now, we may draw the histogram, as shown below.
Note : Since the scale on x-axis starts at 0.5, a kink is shown near the origin.

Class IX, Mathematics, NCERT, CBSE, Important, PDF, Download, Textbook, Statistics

FREQUENCY POLYGON
Let x1, x2, ..., xn be the class marks (i.e., mid points) of the given frequency distribution and let f1, f2, ..... fn be the corresponding frequencies. We plot the points (x1, f1), (x2, f2),..., (xn, fn) on a graph paper and join these points by line segments. We complete the diagram in the form of a polygon by taking two more classes (called imagined classes), one at the beginning and the other at the end, each with frequency zero. This polygon is known as the frequency polygon of the given frequency distribution.

Ex.11 The following table shows the number of diabetic patients at various age groups.

Graphical Representation of Data - Statistics, Class 9, Mathematics | Extra Documents & Tests for Class 9

Represent the above data by a frequency polygon.

Sol. Take two more intervals one at the beginning and the other at the end, each with frequency 0.
Thus, we have class-intervals
0 – 10, 10 – 20, 20 – 30, 30 – 40, 40 – 50, 50 – 60, 60 – 70 and 70 – 80 with corresponding frequencies
as 0, 3, 6, 14, 8, 5, 2, 0 respectively. Thus, we have :

Graphical Representation of Data - Statistics, Class 9, Mathematics | Extra Documents & Tests for Class 9

Now, plot the points (5, 0), (15, 3), (25, 6), (35, 14), (45, 8), (55, 5), (65, 2), (75, 0) on a graph paper and
join them successively to get the required graph.

Graphical Representation of Data - Statistics, Class 9, Mathematics | Extra Documents & Tests for Class 9

 

HISTOGRAM AND FREQUENCY POLYGON ON THE SAME GRAPH

When a histogram and a frequency polygon are to be drawn on the same graph, we first draw the histogram with the given data. We then join the mid-points of the tops of adjacent rectangles by line segments to obtain the frequency polygon.

Ex.13 The following table gives the number of doctors working in government hospitals in a city in various age groups. Draw a histogram and frequency polygon for the given data.

Graphical Representation of Data - Statistics, Class 9, Mathematics | Extra Documents & Tests for Class 9

Sol. 

Step-1 : Draw rectangles with bases 20–25, 25–30, 30–35, 35–40 and 40–45 and heights 40, 60, 50, 20 and 10 respectively. Since the scale on x-axis starts at 20, we make a kink in the beginning. Thus, we obtain the required histogram.

Step-2 : Mark the mid-point of the top of each rectangle of the histogram.

Step 3 : Mark the mid-points of class-intervals 15 - 20 and 45 - 50 on x-axis.

Step-4 : Join the consecutive mid-points by line segments to obtain the required frequency polygon.

Graphical Representation of Data - Statistics, Class 9, Mathematics | Extra Documents & Tests for Class 9

The document Graphical Representation of Data - Statistics, Class 9, Mathematics | Extra Documents & Tests for Class 9 is a part of the Class 9 Course Extra Documents & Tests for Class 9.
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FAQs on Graphical Representation of Data - Statistics, Class 9, Mathematics - Extra Documents & Tests for Class 9

1. What is a graphical representation of data?
Ans. A graphical representation of data refers to the use of visual elements such as charts, graphs, and diagrams to present information or data in a more understandable and visually appealing manner.
2. Why is graphical representation of data important in statistics?
Ans. Graphical representation of data is important in statistics because it helps in providing a visual understanding of complex data sets. It allows us to identify patterns, trends, and relationships between variables, making it easier to interpret and analyze the data.
3. What are the different types of graphs used for graphical representation of data?
Ans. There are several types of graphs used for graphical representation of data, including bar graphs, line graphs, pie charts, scatter plots, and histograms. Each type of graph is used to represent different types of data and variables.
4. How do we choose the appropriate graph for representing data?
Ans. To choose the appropriate graph for representing data, we need to consider the type of data we have and the purpose of the representation. For example, if we want to compare different categories, a bar graph or a pie chart can be used. If we want to show the relationship between two variables, a scatter plot or a line graph can be used.
5. What are the advantages of using graphical representation of data?
Ans. Some advantages of using graphical representation of data include: - It provides a clear and concise visual representation of complex data. - It helps in identifying patterns, trends, and outliers in the data. - It makes it easier to communicate and present data to others. - It enhances understanding and interpretation of the data. - It allows for quick comparisons and analysis of different variables.
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