As a student you will probably have to deal with the weighted and unweighted average, what the mode is exactly, a number of formulas, the mode graphically reading, etc. and not only as a student but as an employer occasionally as well. What exactly does that all mean?
Unweighted average
You can organize and present data from a survey, including in tables and graphs. If you have performed a static survey, it is necessary that you can perform calculations with the data collected. You will then get a better understanding of this data and that is important. And on the basis of that knowledge, important decisions are often made in practice (for example in a company). Sometimes calculations are made that say something about the average value of a certain phenomenon. These calculations indicate the central tendency. The central tendency is the center of gravity and center of the population. The central tendency is about the center (the center) of the data.
In this article you will come across 3 calculations for the central tendency: the unweighted average, the weighted average and the mode. The different values that the phenomenon can assume are added to the unweighted average. This sum is divided by the total number of values. You do not take into account the fact that some values weigh more heavily than others because they occur more often. In practice, we don’t often calculate an unweighted average. The unweighted mean is only correct if each value in the calculation occurs the same number of times in practice. That is usually not the case. In formula: Unweighted mean = Sum of values (W): Number of values.
Weighted arithmetic mean
If you want to know the average price of all sold cards, you have to consider how many cards of each suit have been sold. If the values you calculate an average of do not occur as often, you have to calculate a weighted arithmetic mean. In this calculation you take into account how often a certain value occurs. We call this frequency (F). When calculating a weighted average, you multiply each value (W) by the number of times it occurs (F). You divide the sum of these multiplications by the total number of observations, the total frequency. Weighted Average: SUM (FXW): SUM (F). With a weighted average, you therefore take into account that some values count more heavily in the calculation. This is because they occur more often in practice than other values.
Weighted arithmetic mean for frequency distributions with classification.
Much of the data you come across is divided into classes. Calculating the weighted arithmetic mean for data divided into classes should not pose any problems. In these cases you apply a static rule. This regulates states that all observations in one class are evenly distributed over that class (even if this is not exactly the case in reality). When calculating an average you can then use the class middle. In this calculation you set the values of all observations in one class equal to the middle of that class (for example: class 100 – <200, class middle = 150). The calculation of the weighted arithmetic mean then proceeds in almost the same way as above. You just do not multiply the frequencies (F) by the actual value, but by classes in the middle (M). So you multiply the number of observations in a class by the class middle. You add those multiplications together and divide the sum by the total number of observations. In formula: Weighted arithmetic mean for frequency distributions with class means = Sum (FXM): SUM (F).
The mode
Sometimes it is not interesting to know the mean. For example, you never hear about average income in the Netherlands. You do often hear the term average income. By that you mean the income that is earned by most people. In the Netherlands, the average income is approximately ?? 25,000. Often knowledge about the mean is not that important. It may be more important to know which value occurs most (most often). We call that value the mode. You can quickly determine the mode from a graph. For example, if you display the data from a frequency table in a bar graph, you can find the mode by looking up the value of the highest bar. Even when the frequency table is divided into classes, you can quickly find the mode. The class with the greatest number of observations is the modal class. In that case, the mode itself is the class middle.