Unforgettable Experiences/Activites

This part of the journal is the final chapter. Here, I will state the unforgettable encounters I had with measures of position. So, here I have many things.These are experiences that make mathematics fun and exciting!

The Unknown Path to the Destination

This was when Danielle and I were collaborating to answer our activity in mathematics. We discussed how to get the answer when there was even no formula discussed in the textbook. It seemed like it was up to us to discover. At first, it was really challenging and we had no idea where to begin. It was then we started to explore. In the previous lesson, it was discussed how to get the quartile value of the data using different formulas according to the total number of data. We tried to use those formula but with some variations. Since then, we learned how to get the percentile and decile value of the grouped data. After the activity, we then proceeded to answer some challenging questions in the unit test. There we confirmed further that our newly founded discovery was in fact correct. It was when we started playing, betting on who gets to get the correct answer first. It harnessed our skill to answer and even made shortcuts to answer the problems easier.

Lesson Learned: Be patient because every problem has a solution you will have to discover slowly. To make things lighter, learn how to appreciate even the hardest of problems.

The Sudden Realization

This was when I suddenly realized how to use these measures of position. The first time it was taught which was in 9th Grade Statistics, I never really had much idea on its importance. It was when we had our lesson when I realized how it is used and why to use it. A line in the learning module gave me a reason why to use these measures of position. 

For the Sake of Knowledge...and Research!

I realized that the measures of position can be very important in treating the data. It helps researchers know position of the data in a given set of values. Statistician may want to know the position of a value relative to other values and this is how the measures of position come in.

Other unforgettable experiences include the activities in the learning module that were really challenging. However, I know I'll eventually have more encounters with measures of position, or statistics in general especially when we have our research in senior high school or in college or even beyond that point. At that point, I hope I will make more discoveries that would astound me and eventually increase my interest on this topic!

Difficulties

In this chapter, I will discuss the difficulties I encountered during the course of the lesson about Measures of Position.

Sorting the Ungrouped Data

The ungrouped data are rather basic however, handling these kinds of data requires proper organization because the value of the quantile would be void if the data is not sorted first. Sorting the data in ascending order is challenging especially when done manually and the size of the data is large. The number of data must not also change. When handling ungrouped data, one must be organized to avoid mistakes and repetition of sorting.

Different Formulas for the Ungrouped Data

There are different ways to obtain the quantile of the ungrouped data. The answer of each method may even vary from each other. It is hard to know what method is used to reach the same answer. In real life situation, the formula taught in the 10th Grade Mathemathics textbook "Next Century Mathematics" involved 4 cases. It says that there are different formulas used according to the total number of data. In the learning module, it only involved one formula regardless of the total number of data. This confuses learners on what to use especially when it uses two different kinds of method.

One Missed Step = Repeat from Scratch

 In answering problems of both grouped and ungrouped data, one must remember all required steps to reach the answer. When one forgets to do a step such as sorting, how to identify the quantile class, etc., this could mean the repetition of the solution and the progress you thought you made would be void. One important reminder in getting the quantiles is to be organized at all times to avoid forgetting steps.

There are more challenges and difficulties in the lesson Measures of Position, however, these are more related to statistics in general which involves a greater array of challenges. In my experience, however, the above stated challenges are the highly observed. Though it is tough, it is not hard to answer these kinds of problems. Just follow the steps!

Concept Map

This chapter will show the concept map of the entire lesson. This shows as well the summary of my learning`.

This shows the definition and formula of each of the measure of positions namely quartiles, deciles, and percentiles.

Things Learned and Insights

Measures of Position (Quantiles)

  Measures of position is particularly part of the 10th Grade Kto12 learning curriculum in Mathematics.  A measure of position is a method by which the position that a particular data value has within a given data set can be identified. As with other types of measures, there is more than one approach to defining such a measure. Particularly, there are three measures of position discussed namely percentiles, deciles, and quartiles.

In statistics, quantiles are To summarize my personal learning, I learned these three mentioned measures of position which are closely related to each other, however they may vary in usage according what is required in a problem. 

Quartiles

Quartiles divide a rank-ordered data into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively. The lower quartile Q1 is the value of the variable below which 25% of the cases lie. The Q2 is median score of the data. The upper quartile Q3 is the value of the variable below which 75% of the cases lie.

Deciles

There are nine deciles. These divide the sorted values of the distribution into ten equal parts. It is important to know that D5 is the median score of the data, same as the second quartile. Deciles are useful when dealing with large number of values or quantities. 

Percentiles

Percentiles, on the other hand, are the values that divide a set of data into 100 equal parts. These values are denoted by P1, P2, P3,...P99. In percentiles P50 is the median score of the data. Percentiels are calculated for very large data.

Also, I learned that there are very similar formula to get the measure of position. The functions of each quantile vary according to the size of the data. The following shows the formula to get the quartile of the grouped data.

[MBA Lectures, 2010]

Similar formula can be used for both decile and percentile. We just have to change the divisor of the first term in the parentheses to 10 for deciles and 100 for percentiles.

Overall, the measure of position is very important in statistics, and most especially in research because it helps know where the obtained score of a study or experiment belongs to.