Class 8 Maths Introduction to Graphs Introduction

Introduction:

Graphs are visual representations of data collected. They often helped us in showing the trend of the data. They are used in various fields and it is of immense help to the people. The purpose of drawing a graph is to show numerical facts in usual form so that they can be understood quickly, easily and clearly. There are many kind of Graph and each of these serve specific purpose.

 Class_8_Introduction_To_Graphs_Figure1

A Bar Graph:

 

A bar graph shows comparisons among discrete categories. One axis of the chart shows the specific categories being compared, and the other axis represents a measured value. Some bar graphs present bars clustered in groups of more than one, showing the values of more than one measured variable.

 

Ex: The given bar graph shows Soni’s mathematics marks in the three examinations. Given graph indicates that she has good progress in mathematics.

       Class_8_Introduction_To_Graphs_Bar_Graph

                                               

A Pie Graph (or a circle-graph):

 

A pie-graph is used to compare parts of a whole. The circle represents the whole. A Full Circle has 360 degrees. In a pie chart, the arc length of each slice is proportional to the quantity it represents.

   Class_8_Introduction_To_Graphs_Pie_Graph                                    

In the above pie chart, it shows the percentage of viewers watching different types of TV channels.

 

A Histogram:

 

A histogram is a type of graph that has wide applications in statistics. Histograms provide a visual interpretation of numerical data by indicating the number of data points that lie within a range of values. 

These range of of values are called classes or bins. The frequency of the data that falls in each class is depicted by the use of a bar.  The higher that the bar is, the greater the frequency of data values in that bin.

         Class_8_Introduction_To_Graphs_Histogram      

 

The example above uses $25 as its bin width. So it shows how many people make between $800 and $825, $825 and $850 and so on.

A Line Graph:

 

A line graph, also known as a line chart, is a type of chart used to visualize the value of something over time. The line graph consists of a horizontal x-axis and a vertical y-axis. The point at which the axes intersect is always (0, 0). Each axis is labeled with a data type.

 

Ex: When Radha fell sick then the doctor record the temperature of her body every hour as shown in the table.

 Class_8_Introduction_To_Graphs_Line_Graph

                                 

Now, the line graph is constructed below:

 Class_8_Introduction_To_Graphs_Line_Graph1

                  

Problem: The following graph shows the temperature of a patient in a hospital, recorded every hour:

  Class_8_Introduction_To_Graphs_Line_Graph2                                 

(a) What was the patient’s temperature at 1 p.m.?

(b) When was the patient’s temperature 38.5° C?

(c) The patient’s temperature was the same two times during the period given. What were these two

times?

(d) What was the temperature at 1.30 p.m.? How did you arrive at your answer?

(e) During which periods did the patients’ temperature showed an upward trend?

Solution:

(a) The patient’s temperature was 36.50 C at 1 p.m.

(b) The patient’s temperature was 38.50 C at 12 noon.

(c) The patient’s temperature was same at 1 p.m. and 2 p.m.

(d) The temperature at 1.30 p.m. is 36.5o C. The point between 1 p.m. and 2 p.m., x - axis is

equidistant from the two points showing 1 p.m. and 2 p.m. So it represents 1.30 p.m. Similarly the point

on y -axis, between 360 C and 370 C will represent 36.50 C.

(e) The patient’s temperature showed an upward trend from 9 a.m. to 11 a.m.

 

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