Basic Statistics and Data Analysis

Lecture notes, MCQS of Statistics

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Graphic Presentation of Data

Graphic Presentation of Data

A chart/ graph says more than twenty pages of prose, its true when you are presenting and explaining data. Graph is a visual display of data in the form of continuous curves or discontinuous lines on graph paper. Many graphs just represent a summary of data that has been collected to support a particular theory, to understand data quickly in a visual way, by helping the audience, to make a comparison, to show a relationship, or to highlight a trend.

Usually it is suggested that graphical representations of the data should be carefully looked at before proceeding for the formal statistical analysis, because trend in the data can often be depicted by the use of charts and graphs.

A chart/ graph is a graphical representation of data, in which the data is usually represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart. A chart/ graph can represent tabular numeric data, functions or some kinds of qualitative structures.

Common Uses of Graphs

Presenting the data in graph is a pictorial way of representing relationships between various quantities, parameters, variables. A graph basically summarizes how one quantity changes if another quantity that is related to it also changes.

  1. Graphs are useful for checking assumptions made about the data i.e. the probability distribution assumed.
  2. The graphs provide a useful subjective impression as to what the results of the formal analysis should be.
  3. Graphs often suggest the form of a statistical analysis to be carried out, particularly, the graph of model fitted to the data.
  4. Graphs gives a visual representation of the data or the results of statistical analysis to the reader which are usually easily understandable and more attractive.
  5. item Some graphs are useful for checking the variability in the observation and outliers can be easily detected.

Some Important Points for Drawing Graphs

  • Clearly label the axis with the names of the variable and units of measurement.
  • Keep the units along each axis uniform, regardless of the scales chosen for axis.
  • Keep the diagram simple. Avoid any unnecessary details.
  • A clear and concise title should be chosen to make the graph meaningful.
  • If the data on different graphs are to be measured always use identical scales.
  • In the scatter plot, do not join up the dots. This makes it likely that you will see apparent patterns in any random scatter of points.
  • Use either grid rulings or tick marks on the axis to mark the graph divisions.
  • Use color, shading, or pattern to differentiate the different sections of the graphs such as lines, pieces of the pie, bars etc.
  • In general start each axis from zero; if the graph is too large, indicate a break in the grid.

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Pie Chart |Visual display of categorical data

Pie Chart

A pie chart is a way of summarizing a set of categorical data. It is a circle which is divided into segments/sectors. Each segment represents a particular category. The area of each segment is proportional to the number of cases in that category. It is useful way of displaying the data where division of a whole into component parts needs to be presented. It can also be used to compare such divisions at different times.

Pie chart is constructed by constructed by dividing the total angle of a circle of 360 degrees into different components. The angle A for each sector is obtained by the relation:

$A=\frac{Component Part}{Total}\times 360$

Each sector is shaded with different colour or marks so that they look separate from each other.


Make an appropriate chart for the data are available regarding total production of urea fertilizer and its use on different crops. Let total production of urea is about 200 thousand (kg) and its consumption for different crops wheat, sugarcane, maize, and lentils is 75, 80, 30 and 15 thousands (kg) respectively.


The appropriate diagram seems to be a pie chart because we have to present a whole into 4 component parts. To construct a pie chart, we calculate the proportionate arc of circle, i.e.


Fertilizer (000 kg)

Proportionate arc of the circle



 $\frac{75}{200}\times 360=135$



  $\frac{80}{200}\times 360=144$



  $\frac{30}{200}\times 360=54$



  $\frac{15}{200}\times 360=27$




Now draw a circle of an appropriate radius, make the angles clockwise or anticlockwise with the help of protractor or any other device. For wheat make an angle of 135 degrees, for sugarcane an angle of a44 degrees, for maize, an angle of 54 degrees and for lentils an angle of 27 degrees and hence the circular region is divided into 4 sectors. Now shade each of the sectors with different colour or mark so that they look different from each other. The pie chart of the above data is

pie chart for crops data

pie chart for crops data

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