Basic Statistics and Data Analysis

Statistics Lecture Notes, Online MCQs

Category: Chart and Graphics

Chart and Graphics

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Cumulative Frequency Distribution and Polygon

A cumulative frequency distribution (cumulative frequency curve or ogive) and a cumulative frequency polygon require cumulative frequencies. The cumulative frequency is denoted by CF and for a class interval it is obtained by adding the frequency of all the preceding classes including that class. It indicates the total number of values less than or equal to the upper limit of that class. For comparing two or more distributi0ons, relative cumulative frequencies or percentage cumulative frequencies are computed.

The relative cumulative frequencies are the proportions of the cumulative frequency denoted by crf are obtained by dividing the cumulative frequency by the total frequency (Total number of Observations). The crf of a class can also be obtained by adding the relative frequencies (rf) of the preceding classes including that class. Multiplying the relative frequencies by 100 gives corresponding percentage cumulative frequency of a class.

The method of construction of cumulative frequencies and cumulative relative frequencies is explained in the following table:

cumulative frequency distribution

cumulative frequency distribution

To plot a cumulative frequency distribution, scale the upper limit of each class along the x-axis and the corresponding cumulative frequencies along y-axis. For additional information, you can label the vertical axis on the left in units and vertical axis on right in percent. The cumulative frequencies are plotted along y-axis against upper or lower class boundaries and the plotted points are joined by straight line. Cumulative Frequency Polygon can be used to calculate median, quartiles, deciles and percentiles etc.

Cumulative Frequency Polygon or Ogive

Cumulative Frequency Polygon or Ogive

Basic Statistics / Chart and Graphics

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Pie Chart |Visual display of categorical data

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 a useful way of displaying the data where the division of a whole into component parts needs to be presented. It can also be used to compare such divisions at different times.

A pie chart is 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 colors or marks so that they look separate from each other.

Example

Make an appropriate chart for the data are available regarding the 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 thousand (kg) respectively.

Solution:

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 the circle, i.e.

Crops

Fertilizer (000 kg)

Proportionate arc of the circle

Wheat

75

 $\frac{75}{200}\times 360=135$

Sugarcane

80

  $\frac{80}{200}\times 360=144$

Maize

30

  $\frac{30}{200}\times 360=54$

Lentils

15

  $\frac{15}{200}\times 360=27$

Total

200

360

Now draw a circle of an appropriate radius, make the angles clockwise or anticlockwise with the help of a 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 colors or marks 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

Chart and Graphics

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Scatter Diagram: Graphical Representation for two Quantitative Variables

A scatterplot (also called a scatter graph or scatter Diagram) is used to observe the strength and direction between two quantitative variables. In statistics, the quantitative variables follow the interval or ratio scale from measurement scales.

Usually, in scatter, diagram the independent variable (also called the explanatory, regressor, or predictor variable) is taken on the X-axis (the horizontal axis) while on the Y-axis (the vertical axis) the dependent (also called outcome variable) is taken to measure the strength and direction of the relationship between the variables. However, it is not necessary to take explanatory variables on X-axis and outcome variables on Y-axis. Because, scatter diagram and Pearson’s correlation measure the mutual correlation (interdependencies) between the variables, not the dependence or cause and effect.

Diagram below describe some possible relationship between two quantitative variables (X & Y). A short description is also given on each possible relationship.

Correlation

For more about correlation see the post link below

Correlation: Strength of Relationship between Quantitative Variables
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