Measures of Position

Things Learned and Insights

Measures of Position

I was refreshed with the topic of Measure of Position in our last module for Mathematics 10. Measures of Position are different techniques and ways of dividing a set of data into equal parts. To make the measurements valid, the data must be first arranged in an ascending order, meaning from lowest value to the highest value. There are different types of Measures of Position and they are categorized by how many times they are divided, namely 4 parts or Quartile, 10 parts or Decile, and 100 parts or Percentile.

Quartile

The Quartiles are actually three values, the QI, Q2 and Q3. They constitute the values of 25%, 50% and 75%, in that order. Q2 is also known the median because it determines the middle value or 50%. Q1 is also known as the lower quartile and Q3 as the upper quartile. 

Determining the Quartile:

Ungrouped data

Use the formula:

k(N+1)/4 

where k = nth quartile, where n = 1, 2, and 3. N is for the number.

Grouped data

Use the formula: 

Where:
LB = lower boundary of the Qk class

N = total frequency

cf_b= cumulative frequency of the class before the Qk class

f_q1 = frequency of the Qk class

i = size of class interval

k = nth quartile, where n = 1, 2, and 3

Decile

Deciles are similar to quartiles. But while quartiles sort data into four quarters, deciles sort data into ten equal parts: The 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th and 100th percentiles. D5 constitutes the 50^th rank so it is also the median.

Determining the Decile:

Ungrouped data

Use the formula: 

k(N+1)/10 where k = nth decile, where n = 1, 2, 3, 4, 5, 6, 7, 8, and 9. N is for the number.

Grouped data

Where:
LB = lower boundary of the Qk class

N = total frequency

cf_b= cumulative frequency of the class before the Qk class

f_Dk = frequency of the Qk class

i = size of class interval

k = nth decile, where n = 1, 2, 3, 4, 5, 6, 7, 8, and 9

Percentile

The percentiles are the 99 values of the variable that divide an ordered data set into 100 equal parts.

The percentiles determine the values for 1%, 2%... and 99% of the data.

P₅₀ coincides with the median.

Determining the Percentile:

Ungrouped data:

k(N+1)/100 where k = nth percentile, where n = 1, 2, 3, ..., 99. N is for the number.

Grouped data:

Where:
LB = lower boundary of the Qk class

N = total frequency

cf_b= cumulative frequency of the class before the Qk class

f_Pk = frequency of the Qk class

i = size of class interval

k = nth percentile, where n = 1, 2, 3, ..., 99

Percentile Rank

Percentile ranks are particularly useful in relating individual scores to their positions in the entire group. A percentile rank is typically defined as the proportion of scores in a distribution that a specific score is greater than or equal to.

Determining the Percentile rank

where:

PR = percentile rank, the answer will be a percentage

P cf = cumulative frequency of all the values below the critical value

P = raw score or value for which one wants to find a percentile rank

LB = lower boundary of the kth percentile class

N = total frequency

i = size of the class interval

Answering this topic has become a review session for me because we were taught of this lesson in Grade 8. In our Grade 9, we studied Basic Statistics and it coved the Measures of Position. In our research, we used this topic to acquire the needed data. Now in Grade 10, the lesson was refreshed in our minds.

Concept Map

Difficulties

Measures of Position is a fairly easy lesson in Statistics so the difficulties are quite minimal. For me, the most difficult aspect of Measures of Position is calculating the data in grouped data because aside of a long formula that is very forgettable, the grouped data also consists of other calculations such as the cumulative frequency. In my Grade 9 year, I always mess up my cumulative frequency list so the answer that I’ll arrive into is not exactly the same with the correct answer.

In this case, this lesson mostly prohibits the use of calculators, especially in the exams, and that means that we have to do the calculations manually. With that, there is a higher risk for us to do it mistakenly and thus inaccuracy of the answer. If I forget to solve even just one part, my mind will be surely thrown over and the best option to do is to start everything again. It proves to be very tedious especially if it involves a big set of numbers.

Forgetting to arrange the numbers in an ascending order is the greatest NO NO in Measures of Position because that would change a great aspect in ungrouped data and would deem your solution invalid in grouped data. For me, forgetting to sort the Measures of Position in the correct arrangement is the greatest horror in Statistics because you really need to start all over again. Sorting the numbers can be also forgettable because most of the times in exams, with the overlaying pressure and a limited time, our brains tend to automatically deal the numbers, forgetting the fact that we need to follow some steps fist.

Unforgettable Experiences/Activities

I haven’t answered the Lesson 2 of this module because I joined MTAP but it doesn’t mean that I didn’t experience anything unforgettable in this topic. When I was in Grade 9, Kayla, the reporter of this lesson had tasked us to calculate the Measures of Position for a long table. I started at the top of table and I was devastated to discover that. All my efforts are gone and I swear, I’ll be careful in every calculations I’ll encounter, but of course that wasn’t accomplished. That experience is really unforgettable for me so the next time we answered that type of lesson, I collaborated with my classmates in order to ensure that we will both arrive at the correct answer and at the same time, discuss the parts that we got wrong.