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.