Graphs & Diagrams

Graphs V/S DiagramsGraphs Diagram

Used for studying the relationship between variable

Used for comparison only

Drawn to a particular scale and proportion using lines and points

Represented using bars rectangles ,squares etc

They are more obvious precise and gives more information about the data

They give only approximate information

They are useful in depicting time series and frequency distribution

Can be used only for depicting categorical variables

Different Types of diagrams

• Line Diagram

• Bar Diagram• Pie Diagram

Line diagram

• Simplest of all diagrams

• It Consists of drawing vertical lines, each vertical line being equal to frequency

• ‘X’ values are presented on a suitable scale along the ‘X’ axis, corresponding frequencies are presented along the ‘Y’ axis

Line diagram

Bar Diagram• Most commonly used devices of presenting most of

the business and economic data. • Especially satisfactory for categorical data or series.

They consist of a group of rectangles, one for each group or category of the data in which the values or the magnitudes are represented by the length or height of the rectangles, the width of the rectangles being arbitrary and immaterial. These diagrams are one-dimensional because in such diagrams only one

• dimension viz.; height (or length) of the rectangles is taken into account to present the given values.

Simple Bar Diagram

Component Bar Diagram

• Subdivided bar-diagrams are useful not only for presenting several items of a variable or a category graphically

• Enables us to make comparative study of different parts or components among themselves and also to study the relationship between each component and the whole.

Represent the following data by a suitable diagram

Percentage Bar Diagram• Percentage bar diagram is used to highlight the

relative importance of the various component parts to• whole. The total for each bar is taken as 100 and the

value of each component or part is expressed, percentage of the respective totals. • In a percentage bar diagram, all the bars will be of the

same height, viz., 100, while the various segments of the bar representing the different components will vary

in height depending on their percentage values to the total.

• Percentage bars are quite convenient and useful while comparing two or more sets of data.

Example:-Percentage Bar Diagram

Draw a percentage bar diagram torepresent the following data??

Pie Diagram• The circle representing the total magnitude

may be divided into various segments • Each sectors representing certain proportion

or percentage of the various component parts to the total. Such a sub-divided circle diagram is known as an angular or pie diagram.

• Named so because the various segments resemble slices cut from a pie.

Pie Diagram

• Draw a circle of appropriate radius.• Draw any radius preferably horizontal one.• Degree of any component part is given by

• Draw a line segment from the centre of the circle at an angle given by the component part.

• Different sectors are represented by different shades and colours.

Example:-Pie Chart

Draw a Pie chart for the following three five year plans and compare the

results

Histogram

• One of the most popular and commonly used graphs for charting continuous frequency distribution.

• It consists in erecting a series of adjacent vertical rectangles on the sections of the horizontal axis (X-axis), with bases (sections) equal to the width of the corresponding class intervals and heights are taken in such a way that it equals to frequencies of the corresponding classes.

HistogramVariable Frequency

10-20 12

20-30 30

30-40 35

40-50 65

50-60 45

60-70 25

70-80 18

Histograms with Unequal Class Width

• If all the classes are not uniform throughout; as in case the different classes are represented on the X-axis by sections or bases which are equal the magnitudes of the corresponding classes and the heights of the corresponding rectangles are to be adjusted so that the area of the rectangle is equal to the frequency density of the corresponding class

Bars are different in width

Histograms with unequal class interval

• This adjustment can be done by taking the height of each rectangle proportional (equal) to the corresponding frequency density of each class which is obtained on dividing the frequency of the class by its magnitude

FREQUENCY DENSITY = Frequency Class width

Question:-The frequency distribution of the speeds maintained by vehicles in the

highways are given below..

Speed, kph 0< v ≤40 40< v ≤50 50< v ≤60 60< v ≤90 90< v ≤110

Frequency 80 15 25 90 30

Classes

Draw a histogram for the following data

Speed, kph 0< v ≤40 40< v ≤50 50< v ≤60 60< v ≤90 90< v ≤110

Frequency 80 15 25 90 30

Frequency Density

Class width 40 10 10 30 20

2.0 1.5 2.5 3.0 1.5

Frequency Densities

0 4020 60 80 100 120

3.0

2.0

1.0

Freq

Den

s

Speed (kph)

Frequency = Width x Height

Frequency = 40 x 2.0 = 80

Bar Graph HistogramOne dimensional graph Two dimensional graph

Frequencies represented by the height of the bar

Frequency density given by area of the bars.

Spacing b/w the graphs, discrete

Bars are adjacent to each other, continuous

Can be used only for depicting categorical variables

They are useful in depicting time series and frequency distribution

Difference b/w histograms & bar diagrams

Frequency Polygon

• Frequency polygon is another method to graphically represent a frequency distribution.

• They can be drawn directly by taking frequencies on Y-axis and midpoints of corresponding classes against X-axis and joining the points by straight lines.

• They can be also draw from histograms by joining the midpoints of each bars of the histogram.

Discrete Variables Continuous Variables

Frequency Polygon

Ogive or Cumulative Frequency Curve

• It is a graphical representation of cumulative frequency curve.

• It consists in plotting the c.f (along the Y-axis) against class boundaries (along X-axis).

• we have two types of ogives, (i) 'Less than' ogive. (ii) 'More than' ogive.

Example: Convert the following less than frequency distribution to more than frequency distribution and draw

both the ogives

Assignment:- Construct a frequency distribution of the data taking class width of 10 and draw a histogram, frequency polygon and construct both the ogive

curves

6732583765

Stemplot (Stem-and-Leaf Plot)

• A stem and leaf diagram is a good way to obtain an informative visual display of a data set of numbers which consists of atleast two digits.

• Divide each number into two parts, a stem consisting of one or more of the leading digits, and a leaf, consisting of the remaining digit.

• List the stem values in a vertical column• Write each leaf in the row to the right of its

stem, in increasing order out from the stem.

Example:-The following data set contains the midtermexam scores of STAT 101.

74 76 78 88 87 87 53 95 82 79 79 78 62 80 77 70 60 60 84 95 85 93 79 84 71 85 100 77 72 95 79 83 97 87 73 84 74 83 85 95 62 50 86 83 86 36

Stem and leaf diagramA stem-and-leaf display is follows:

3: 64 :5 : 036 : 00227 : 0123446778899998 : 023334445556677789 : 35555710 : 0

Draw a stem and leaf plot for the following data

Stem and leaf diagram