Organisation and Presentation of Data (Part 2)

Important points to remember while drawing a chart:

• The title of the graph should be clear.
• Axes should be well labelled. 
• Unit of measure should be clearly stated in the axis.
• A legend is necessary to differentiate between graphs.

Bar chart

A bar chart is a diagram in which the numerical values of variables are represented by the height or length of lines or rectangles of equal width.

The advantage of a bar chart is that it is a versatile and adaptable instrument. For example, a bar chart can be represented for positive values as well as negative values.

Example of a bar chart.

Compound/component bar chart

• A component bar chart has each bar representing a class and splits up into components. Within each bar, components are always stacked in the same order.
• It is desirable that the component bar chart does not contain too many components, or else, the impact on the reader may be blurred.
• Whenever there is a need to compare 2 data sets using component bar charts, it is advisable to use percentages rather than actual numbers.
• Percentages make comparison easier, especially when diagrams are used.

Used particularly when class totals need to be represented (Adv)Not easy to compare components relatively across classes owing to actual values being displayed. (Disadv)

Multiple bar chart

Multiple bar charts have a set of bars for each class, each bar representing a single component of the total. Within each set the bars are physically joined and always arranged in the same sequence. Sets of bars should be separated.


Good for comparing components both within and across classes in actual terms, since each bar is drawn from a fixed base (Adv)Class totals are not easy to assimilate (Disadv)

Pie chart

• The main objective of a pie chart is to show the relative importance of the component parts of a total.
• The pie chart is drawn for categorical data.
• The pie chart is not an appropriate graph if there are too many components.

Histogram

• The width of each bar is proportional to the size of the class it represents
• The quantity on the vertical axis is in some cases called the frequency density
• The horizontal axis must have a scale
• The area of a bar is proportional to the frequency.

Ogive curve

Instead of considering the frequency of each class, we may consider the frequency with which the variable falls below a particular value.

Semi logarithmic graph.

—A logarithmic graph, is a graph where the scales on the horizontal and vertical axes are in logarithmic scale.

A semi-logarithmic graph is one, where an axis is in logarithmic scale.

How to make a semi logarithmic table and graph

—

1. By plotting a semi-logarithmic graph, the rate at which the price is moving becomes clear.

2. A logarithmic graph can also be used when the figures with which we are concerned range so 

  widely that it is inconvenient to use a “normal” graph.

Lorenz curve

The Lorenz curve is used in economics and ecology to describe inequality in wealth or size. The Lorenz curve is a function of the cumulative proportion of ordered individuals mapped onto the corresponding cumulative proportion of their size.

EXAMPLE:

Any divergence from the straight line indicates that there is inequality in the distribution of incomes among income earners

—If the lorenz curve is below the straight line, the inequality is in favour of the upper income groups in that a high percentage of low income earners receive a small percentage of income

The Z curve

• —The Z chart is merely a device to enable management to show concisely three different aspects of  a time series plotted on one graph.
• —On the bottom bar of the Z, we plot the time series of monthly (or weekly) sales, or output or whatever variable we are considering
• —On the diagonal bar of the Z, we plot the cumulative total to date that is, the total sales or output we have achieved since the beginning of the year.  
• —On the top bar of the Z, we plot the moving annual total sales (for e.g. total sales achieved during the period 1February last to 31 January this year; the February figure is the total from last March until the end of February this year, etc.)

Scatter diagram

—       The scatter diagram is one which tries to ascertain if there is a relationship between two quantitative variables.

There can be a direct relationship (when X ↑ , Y ↑) or an inverse relationship (when X ↑ , Y ↓)

The data displayed on the graph resembles a line rising from left to right.  Since the slope of the line is positive, there is a positive correlation between the two sets of data.  This means that according to this set of data, the longer I study, the better grade I will get on my Regents examination.