Statistics refers to the use of data analysis to solve management problems for effective decision making supported by the conclusions drawn from empirical evidence. In Statistics, we must collect and organize the data, summarize and analyze the results, in order to interpret and present the numerical data. In the last lesson, I covered summarizing and analyzing the data. In this lesson, I’ll cover interpreting and presenting the results.
One of the most crucial aspects of interpreting statistical data is measuring the results as either absolute or relative. Absolute data refers to the actual numerical value, whereas relative data refers to the percentage such data accumulates of the entire sample of data. For instance, in a class room there may be 13 males and 17 females in which 13 and 17 are the absolute values of the total 30 sample size. Of that sample size 13 males accounts for 43.3% of the sample and 17 females accounts for 56.7% of the sample, together these two categories of the sample size accumulates to the full 100% of the sample data. The chart that most benefits off such interpretation is the Pie Chart. Pie Charts are one of the most visually appealing methods of presenting statistical data because of its simplicity. A Pie Chart shows the proportion or percent that each class represents of the total number of frequencies. So essentially a Pie Chart is a division of specified categories like the previous example of males and females in a sample, and the categories in summation equate to 100% of the Pie. You can see a Pie Chart I’ve made for the gender of a class example below.
Bar Charts and Histograms are also a visually appealing method of presenting statistical data, however they are more commonly utilized for more categories and benefit more from absolute data of interpretation. A Bar Chart is a graph in which the classes are reported on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars. So essentially the categories are listed on the x-axis and the values are listed on the y-axis, each category is valued at its height which corresponds with its associated value of frequency. Bar Charts and Histograms have three main differences: Histograms are more so utilized to show distribution between categories while Bar Charts are used to compare categories; Histograms plot grouped quantitative data while Bar Charts plot categorical data; and Bars can be reordered in Bar Charts unlike Histograms. Two examples are displayed below, the left Bar Chart represents class rank and the right Histogram represents GPA range.
There are of course other less visually appealing graphs like scatter plot diagrams and their accompanied regression lines I covered in the last lesson, but there are also more advanced graphs for presenting statistical data like Frequency Polygon Charts. A Frequency Polygon Chart shows the shape of a distribution similarly to a Histogram but can compare more than one entirely different subjects like Study Time and Work Hours in one chart as shown below. This method of presenting statistical data is highly invaluable to those comparing two or more subjects. It is done by gathering data in a Frequency Table which I explained briefly in the first lesson, however I’ll explain the method more in this lesson. A Frequency Table is a grouping of qualitative data into mutually exclusive classes showing the number of observations in each class. Therefore using the example below, data is gathered on students representing how many hours they spend studying and working per week. The students’ data are then organized into hours between 5-9, 9-13, 13-17, 17-21, and 21 and above. This Frequency Table resulted in 9 students studying between 5-9 hours, 8 students working between 5-9 hours, and so on. After the Frequency Table was complete, I made a scatter diagram of the organized data with straight lines and markers to create the Frequency Polygon Chart which resulted in the following chart below.
My professor didn’t focus on teaching us highly advanced techniques of statistics, but rather drilled us to learning the basics well. I actually went a bit too far making this Frequency Polygon Chart, because when my professor checked over my work he explained that integrating two subjects like Study Time and Work Hours would be too advanced for the class; and so I had to separate the graph into each respective subject in order to receive full credit on my assignment. He also highly preferred Histograms to Bar Charts, and made sure we knew the proper terminology of statistics by incorporating a written portion of all of our tests. Overall, the statistics course I took last year was beneficial for my practical understanding of statistics and not for teaching me fancy techniques that wouldn’t translate into the real world. If you enjoyed this Statistics series, please leave a like at the top of the article and I’ll do my best to do so again for other topics. I’m planning to close out the year with Digital Waypoint’s longest running series yet, focusing on Marketing so stay tuned.
Image:http://www.energyteam.co.uk/media/104732/Statistics.jpg
