Visual Presentation of data

In order to be useful, data must not only be organised, but it should also be able to be represented in some way that comparisons, trends and or relationships may easily be visualised.

Graphs and charts provide such representations. “A picture is worth a thousand words”

A diagrammatic or graphical display reveals the main characteristics of a set of data at a glance. Visual communications can be understood by both literate and illiterate people.

Graph Vurses Chart /Diagram

Advantages of Graphs & Charts

A diagram or chart makes an immediate visual impact.

More attractive, create a long lasting impression

Make a large and unmanageable data understandable.

We can determine some of the measures of location, like median and mode, no need of formula.

Need much less time in drawing inferences

Allow us to make quick comparison of two or more sets of large data.

Disadvantages of Graphs & Charts

Serve only as a supplement of table, not an alternative to it

Difficult to choose the correct formats available for creating charts and graphs

Fail to exhibit small differences so not good for accuracy

Charts and graphs are costly

General rules for constructing diagrams

1. Serial number : It is necessary when there are more than one graph or diagram

2. Title: It should be brief and self-explanatory

3. Axes : Dimensions in the data are often displayed on axes

4. Size and scale : Size of the graph and diagram should match the size of the paper and scale should always be mentioned

5. Clear and simple: Too much information on the graphs and diagrams should be avoided

6. Legend : When chart represents data on multiple variables, it should have a legend

7. Footnote: It clarifies certain points in the diagram.

8. Source : Generally mentioned at the bottom about source from where the information put in the graph have come

Types of charts, graphs and diagrams

Line graphs

It is generally used to show how something changes over time

When it is prepared for data on time series, called as time series plot.

It uses line segments to connect data points and shows changes in data over time

Normally used to display the relationship between two variables such as X and Y.

Preparation of a line graph

1. Data points are entered in a graph

2. Horizontal line is called the horizontal axis

3. Vertical line is called the vertical axis

4. Once the data points have been entered, they are connected by a line.

A line diagram of body weight under the influance of different quantity of feed additive

Bar chart or bar graph

A bar chart is defined as a graph made of bars whose heights represent the frequencies of respective categories.

Bar graphs are commonly used to depict the relationship between two or more series of categorical data.

These are used to compare things between different groups or to track changes over time.

The bars can be either vertical (up and down) or horizontal (across)

A bar graph has two axes. One axis describes the types of categories being compared, and the other describes the numerical values that represent the data.

Bar graphs are good for plotting data that spans many years (or days, weeks . . .), has really big changes from year to year (or day to day . . .)

Bar graphs are best suited for a qualitative independent variable.

Categories are represented along the horizontal axis (abscissa, or X axis), and frequencies are represented along the vertical axis (ordinate, or Y axis).

The zero point or origin of the vertical axis is located at the X and Y intercept, i.e., the point where the two axes cross.

The bars can be of any width, but they should not touch each other. A space between the bars emphasises the discrete, qualitative character of the class intervals.

Bar graphs are good for plotting data that spans many years (or days, weeks . . .), has really big changes from year to year (or day to day . . .)

Bar graphs are best suited for a qualitative independent variable.

Categories are represented along the horizontal axis (abscissa, or X axis), and frequencies are represented along the vertical axis (ordinate, or Y axis).

The zero point or origin of the vertical axis is located at the X and Y intercept, i.e., the point where the two axes cross.

The bars can be of any width, but they should not touch each other. A space between the bars emphasises the discrete, qualitative character of the class intervals.

Types of bar charts

Bar chart for data on one independent and one dependent variable

Simple bar chart

When there is data for only one categorical variable.

A bar graph is said to be one-dimensional because only the heights of the bars or rectangles are important which depend on the requencies of various categories.

Example: Prepare a bar chart of total lactation milk yield of Kankrej cows recorded during different years from the data given in Table.

Bar chart for data on two (or more) independent variables and one dependent variable

Multiple or grouped bar chart

The data comprises of two or more categories or groups. Example, the milk yield of two or more breeds of cows, body weights of male and female animals, production of certain commodity during different years, etc.

Component bar chart

Also known as divided bar diagram. The bars are represented by the frequencies of different components.

It is also referred to as stacked bar chart because the components corresponding to a particular category are put on the same bar in stacked style.

Percent bar chart

Very similar to component bar chart with the only difference that instead of components of various items, the percentage of each variable is taken into account for erecting the bars.

In case of percentage bar diagram, the height of the bar is equal to 100 and its divisions correspond to the percentages of various items included in the study.

Pie charts or circle graphs

Shaped like a circle

Useful to show the proportion of certain types of data as parts of a whole

The "pie" represents the whole,

The segments of the pie represent the proportion of various data points to that whole.

It gets its name by how it looks, just like a circular pie that has been cut into several slices.

Defined as a circle divided into portions that represent the relative frequencies or percentages of a population or a sample belonging to different categories

Unlike bar graphs and line graphs, pie charts do not show changes over time.

Pie charts are best to use when we are trying to compare parts of a whole

A pie piece, representing a given category, is a portion of the circle called sector.

The angle of a sector is proportional to the frequency of the data.

Because a circle has 360 degrees, we need to multiply percentage of a category by 360 to get an angle of the sector corresponding to that category.

Angle of a sector = (Frequency of class/Total frequency)360 degree

Pie chart showing population of different breeds of buffaoes in India

Limitations of pie diagram

If there are too many categories, then there will be a multitude of pie pieces.

we want to compare different categories that are close in size, then a pie chart will not be the diagram of choice

Scatter plot

The scatter plots are used to see if one event affects another event

The X-Y plots are used to determine relationships between the two different things.

The x-axis is used to measure one event (or variable) and the y-axis is used to measure the other.

If both variables increase at the same time, they have a positive relationship

If one variable decreases while the other increases, they have a negative relationship.

Sometimes the variables don't follow any pattern and have no relationship.

Histogram

Similar in appearance and construction to a bar graph, but it is used for a frequency distribution of a continuous quantitative variables rather than qualitative variables.

Constructed by erecting vertical bars over the real limits of each class interval, with the height of each bar corresponding to the number of scores in the interval.

The bars of adjacent class intervals touch each other leaving no space between the bars.

This emphasises the continuous, quantitative character of the class intervals.

Construction

The class intervals are represented along the horizontal axis, and frequency is represented along the vertical axis.

A bar is drawn for each class so that its height represents the frequency of that class.

The bars in a histogram are drawn adjacent to each other. Thus, unlike the bar charts which have gaps between the bars, there is no gap between bars in a histogram.

The zero point or origin of each axis is located at the X and Y intercept.

The height of the graph is 66% to 75% of its width, and

The two axes are labelled appropriately, and a figure caption is given to help the reader interpret the graph.

When to use a histogram?

To represent continuous data,

To represent data expressed as actual numbers, percentages and frequencies.

If we get more information from a chart where the classes are of different sizes.

Frequency polygon

A frequency polygon is constructed from the frequency distribution such that the horizontal axis is marked off into class intervals, and the vertical axis is marked off into numbers representing frequencies. However, the frequency of a class is not represented by a vertical bar but by a dot placed at the proper height over the midpoint of the class interval.

Then we join the adjacent dots with straight lines. The resulting line graph is called a frequency polygon or simply a polygon.

Polygon is used to present quantitative data in graphic form

Similar to histogram, a polygon with relative frequencies marked on the vertical axis is called a relative frequency polygon, whereas a polygon with percentages marked on the vertical axis is called a percentage polygon.

Frequency curve

A frequency curve is drawn by connecting the dots placed over the top of midpoints at the height corresponding to the frequencies of the class intervals by a smooth hand (not in a straight line).

For a very large data set, as the number of classes is increased (and the width of classes is decreased), the frequency polygon eventually becomes a smooth curve.

Cumulative frequency curve or ogive

It is a line graph of a cumulative frequency, also called as cumulative polygon

Depending upon the type of cumulative frequencies constructed, we can create two types of ogives

– one less-than and

- more-than.

Every ogive starts on the left with a cumulative (or relative) frequency of zero at the lower class boundary of the first class and ends on the right with a cumulative relative frequency of 1.00 (or 100%) at the upper class boundary of the last class.

The cumulative polygon has the characteristic “S” shape that occurs whenever there are more scores in the middle of the frequency distribution than at the extremes. Graphs that are “S” shaped are called ogives.