A vital part of the scientific method is being able to analyze your results and observations (data) so that you can form a sound conclusion. This is basically performed through two means of analyses: qualitative analysis and quantitative analysis. Qualitative analysis is not based on measurements, rather it is a means of analysis that provides your observation; for example, “what components were found in a sample,” or “whether an experimental group of plants performed better than the control group of plants.” Quantitative analysis, on the other hand, is based purely on measurements and always involves numbers—for example, “how much of a given component is present in a sample,” or “how much the experimental group of plants grew in comparison to the control group of plants.” While qualitative analysis is important to the explanation of your results, it is quantitative analysis that truly expresses your ability as a student scientist to interpret your data in a more precise and objective way that will provide a useful means for the interpretation of your conclusions by others. The remainder of this chapter is devoted to the interpretation, use, and explanation of the numerical data you have gathered from your experiment.

A very important part of explaining your results and observations to others is by giving meaning to your numerical data and the conclusions you formed from it. Since you began your experiment, you have been gathering data. Data are essentially groups of figures for a given experiment. During the initial stages of an experiment, they may have little meaning so it is important that you compile and organize your data accurately for your final analysis, observations, and conclusions. A good way to keep data is to record them in your project journal. After you have written down all the experimental results in an organized way, you can easily refer to your results to make generalizations and conclusions. There are several methods of presenting data, including the basic tabular, graphic, and statistical methods.

### Tabulating and Graphing

Raw data have little or no meaning in and of themselves. It is only when they are organized into tabular and graphic forms that they can be understood in terms of your project. The data results must be arranged so that a project observer or judge can quickly comprehend the results of the project at a glance. Tables are relatively simple to make and convey information with precision. Additionally, they form the basis for most graphs. The main points to consider are organization and coordination. For example, consider these recordings in tabular form of the body temperature of a flu patient:

If you want to see how the patient’s temperature fluctuated during the day, you can do this by analyzing the table. But if you wanted to see at a glance how the patient’s temperature changed, a graphic representation would be more effective.

A line graph may be used for this analysis. A line graph is composed of two axes: the x, or horizontal, and the y, or vertical. The x axis contains all the points for one set of data, and the y axis contains all the points for the other set of data.

For example, you could label a range of body temperatures on the y axis and label the times on the x axis. After your axes are labeled, simply plot the points. Plotting involves matching each temperature with the corresponding time and marking them on the graph. For example, at 6:00 A.M. the body temperature was 97 degrees Fahrenheit, so you should locate and mark the point on the x and y axes at which 6:00 A.M. and 97 degrees correspond. Then do this for the rest of the data and connect the points to complete the graph.

From this graph, we can quickly see that the patient’s body temperature rose gradually, peaked late in the day, and fell during the evening. Another means of graphical representation that makes data easy to understand is the pie chart. Suppose that you are testing a specimen of blood to determine the percentage of its composition of erythrocytes, leukocytes, and thrombocytes. After several tests and microscopical observation you conclude that the blood contained the percentages shown in the following table:

Each section represents a percentage of the pie. It is easy to see that the leukocyte blood count is low in terms of its percentage of the total composition. There are many other ways to graph your data besides the two methods shown. The important thing to remember about graphing is that it summarizes your results in a visual form that emphasizes the differences between groups of data results. As the old saying goes, a picture is worth a thousand words. The Statistical Method Some very simple statistics will allow you to expand on your data analysis. Some of these applications include: the mean, frequency distribution, and percentile. The mean, expressed as x–, where x is any rational number, is a mathematical average that is really the central location of your data. The sum of your data numbers is denoted by the symbol Σ, which means “the summation of.” This sum is then divided by the quantity of your data recordings,which is the symbol n. Thus the mean is expressed as this formula:

Using the formula, you can express your results as follows: If Σ (x) = 9.24 and n = 11, then x – = 9.24/11 = 0.8400. The figure .8400 is the mean, or the mathematical average, of the studied water plants. Now suppose that you collected samples from 50 water plants. It may be difficult to generalize about the results, so a better method is needed to record the data. One way of describing the results statistically is with a frequency distribution. This method is a summary of a set of observations showing the number f items in several categories. For example, suppose that the following levels were observed to be present in 50 samples:

These results can then be graphed using a histogram, which represents your frequency distribution. With a histogram, your item classes are placed along the horizontal axis and your frequencies along the vertical axis. Then rectangles are drawn with the item classes as the bases and frequencies as the sides. This type of diagram is useful because it clearly shows that the fluoride levels are normally at the 0.90 to 1.00 ppm mark (see diagram).

The percentile is another useful statistic. A percentile is the position of one value from a set of data that expresses the percentage of the other data that lie below this value. To calculate the position of a particular percentile, first put the values in ascending order. Then divide the percentile you want to find by 100 and multiply by the number of values in the data set. If the answer is not an integer (a positive or negative whole number), round up to the next position of the data value you’re looking for. If the answer is an integer, average the data values of that position and the next higher one for the data value you’re looking for. For example, suppose that you wanted to test the efficiency of 11 automobiles by measuring how many miles each car gets to a gallon of gasoline. You have recorded the following data: 17.6, 16.4, 18.6, 16.1, 16.3, 15.9, 18.9, 19.7, 19.1, 20.2, and 19.5. First, you would arrange the numbers in ascending order: 15.9, 16.1, 16.3, 16.4, 17.6, 18.6, 18.9, 19.1, 19.5, 19.7, and 20.2. Now suppose that you want to determine which car ranked in the 90th percentile. To calculate the 90th percentile for this data set, write this equation: (90/100)(11) = 9.9. Since 9.9 is not an integer, round up to 10, and the tenth value is your answer. The tenth value is 19.7; therefore, the car that traveled 19.7 miles per gallon of gasoline is in the 90th percentile, and 90 percent of the cars in your study were less gas efficient.

In summary, you will have to decide which technique works best for your type of data. You can usually express your results in terms of either standard mathematical or statistical graphing. However, there are occasions when only one type will work. If you are dealing with numerous figures or classes of figures, a statistical graph usually works best. For example, if you wanted to demonstrate the variation of test scores between boys and girls in the eighth grade, you would probably make your point clearer by using the statistical method, which would allow you to find the percentiles in which each student scored and the mean test score. On the other hand, if you were investigating the mineral composition of water, the best way to represent the proportion of its contents might be through a pie chart.

### Other Means for Representing Data

Since every project is different you may find that you will need other means for showing and explaining your data results. For example, if you need to refer to various stages of a science project experiment that was conducted over a long period of time where measurements may have been taken at various stages at specific times, a time line might be a better means of representing your data (see the diagram below). Additionally, if you need to describe the results of a repeated process or a sequence and it is cumbersome to do so through text, a series of flow charts may be useful and may make your project data results visually interesting.

### Summary

1. Data are groups of figures or results you recorded from conducting your experiment. They are organized for observation and drawing conclusions about your experiment.
2.  The tabular, graphic, and statistical methods are some of the basic ways of calculating and presenting data.
3. 3. Some basic ways to show your data so that others can see your results at a glance are through the use of line graphs, pie charts, bar graphs, time lines, and flow charts.