Descriptive vs. Inferential Statistics

When we think of descriptive statistics we often think of the process of analyzing data. This data is able to explain, present and sum up information in a way that shows how trends and patterns come from that data. What this type of descriptive statistics doesn’t allow us to do is draw conclusions. It is the type of statistics that enables us a clearer and simpler way to describe the gathered data.

Descriptive Statistics

It is a crucial component of statistics. This is because it would be hard to visualize and the raw data. This can be quite a laborious job to do especially if there is a lot of data. This is where descriptive statistics comes into play. It gives us the opportunity to showcase the data in a much more meaningful way. This allows the data to be interpreted more coherently.

For instance, if there are results of one hundred pieces of coursework of students, the goal is to analyze the overall performance of those same students. Another goal is to distribute and spread the received marks. This is what descriptive statistics enables us to do.

There are two types of statistics that are used when describing data.

1. Measures of central tendency – There are ways for a group of data to define the central location of a frequency distribution. Throughout this scenario, the spread of frequency is essentially the distribution and pattern of marks scored from the lowest to the highest by the 100 learners. Using a variety of statistics, including the mode, median and mean, we can define this central location.

2. Measures of spread - There are ways to sum up a collection of data by explaining how the scores are spread out. The mean score of our 100 students, for instance, might be 95 out of 100. Not all students, however would have earned 65 marks. Rather, it will spread out their ratings. Others are going to be lower and some higher. Spreading tests allow us to summarize how these ratings are distributed out. A variety of statistics are available to us, including the distribution, interquartile range, absolute variance, range and standard deviation, to explain this spread.

If we want to use descriptive statistics, it's indeed useful to use a combination of management process (i.e. tables), reported that the results (i.e. graphs and charts) and statistical commentary to summarize our data group (i.e., a discussion of the results).

Common tools of descriptive statistics

Central tendency: To find the middle of the dataset, use the mean or median. You are informed by this calculation where most values fall.

Dispersion: So where does the data stretch from the middle? To calculate the distribution, you can use the spectrum or standard deviation. A low dispersion means that around the center, the values cluster more tightly. Higher dispersion means that farther away from the middle, data point’s drops. We can graph the distribution of frequency, too.

Skewness: The indicator informs you whether there is a symmetric or distorted distribution of values.

Using both numbers and maps, you may present this summary information. These are the basic descriptive statistics, but you can perform other descriptive analyses, such as analyzing the paired data relationships using correlation and scatterplots.

Inferential Statistics: Inferential statistics take a sample's data and draw conclusions about the wider population from which the sample was taken. Since the purpose of inferential statistics is to draw conclusions and generalize them to a population from a sample, we need to have faith that the population is correctly represented in our sample. Our process is influenced by this necessity. We must do the following at a wide level:

1. Define the population we are studying.

2. Draw a representative sample from that population.

3. Use analyses that incorporate the sampling error.

We don't get a convenient party to choose. Random sampling, instead, helps one to have assurance that the population is described by the survey. This approach is a predominant way of collecting samples that reflect the majority population. Random sampling generates statistics that don't appear to be too high or too low, such as the average. We can generalize from the sample to the larger population, using a random sample. Unfortunately, it can be a complex method to collect a completely random sample.