Flowcharts and Histogram

Flowcharts

A flowchart provides a visual representation of a sequence of operations in a process. It is not a statistical tool, but is very commonly used to depict algorithms or processes. Flowcharts help with the design and analysis of a process. The act of mapping a process into steps not only increases ones understanding of the process but may also show areas of improvement. Flowcharts can be used to describe a single process or multiple processes. A good flowchart is one that is easily understood without the need for any further explanations of the process. A flowchart is made up of different shaped boxes that represent different functions. But its most commonly used symbols are  The elongated circles which indicate the start or end of a process Diamond shaped box which indicate a decision box which usually has two outputs  Rectangular boxes which represent a single action or a set of actions  A circle which acts as a connector, to be used when connecting two flowcharts The first step to drawing a flow chart is a brainstorming session to determine the different tasks that occur during a process. These tasks must then be lined in the correct sequence, making sure to cover all paths a process could take, for e.g. you must constantly ask yourself “should a decision be made here?” In this way the whole flow of actions can be worked through by putting appropriate decision boxes wherever necessary. The end of the process must be marked with a “finish” box. A basic flowchart diagram is shown here. Histograms Histograms are a form of bar chart, usually used to measure frequency distribution of data. The groups of data are called bins because each bin represents data points within a particular range. Constructing a Histogram Some steps for construction of a histogram are: Data gathering: There must be enough data or samples for good results. For an accurate Histogram, there must be at least 50-100 data points. Count the number of data points (N). Compute the range of data: Divide the range of the sample data obtained on the X-axis. Calculate the range(R) as the largest point – smallest point. This is an important step to maintain the accuracy and effectiveness of the histogram. You may have to round off the range to make it a more convenient number to plot. Draw the x – and y – axes on a graph paper. Mark the data ranges on the x-axis and the count on y-axis. The data ranges will be the bars/bins of the histogram. The number of bins (B) = Sqrt of (N). Each bin size(S) = (R)/(B) Plot the sample data on the graph. This sample data will determine the height of each bar in the graph. Consider the marks of obtained by the students of a classroom. Suppose the minimum score were 0 and maximum score were 100, then the range would be 100-0= 100. The table marks range against the count is as shown: When to use a Histogram ? A histogram may be useful in multiple instances. Below are some of them:  When dealing with numerical data.  To communicate the distribution of data  To judge the difference between the outcome of two processes  Analysis of the output of a process Histograms express data in a graph such that it provides with the type of the curve of frequency distribution and modality. The numbers of bins in a histogram are important. Fewer bins - which mean wider bins - in a histogram, may result in important information going unnoticed. Whereas too many bins can be misleading because what may seem to be significant information can simply be due to random variations that occur due to small number of data samples in the bin. To avoid making either mistake, vary the bin widths while plotting a histogram. A histogram simply sums up data and displays it in a more concise manner. However, it does not give solutions to problems. It is only a first step towards problem solving. The results of a histogram depend heavily on the date and how updated the data of the histogram is. If there are any inconsistencies in the data, then the histogram will also be inaccurate.