DIFFERENT TYPES OF DATA

The Partition Values are the measures or values used in statistics for dividing the total number of observations of distribution into a certain number of equal parts. . Commonly used partition values are Quartiles, Deciles, and Percentiles, these are the topics we will be discussing today. It is important that the data should be sorted in either ascending or descending order before calculating the partition values.

• Quartile – divide any given data into four equal parts

• Decile – divide the given data into ten equal parts

• Percentile – divide the given data into hundred equal parts

These partition values are used to split the data and distribute it into smaller parts which makes it easier to measure, analyze and understand. In the following sections, we will learn all we need to know about the types of data in partition values.

Quartiles:

The quartiles divides any given data set into four equal parts. There are three quartiles the First Quartile (Q1),  The Second Quartile (Q2), and The Third Quartile (Q3) which divide the given data into four equal parts, with one-fourth of the data values in each part. The Q1, Q2, and Q3 are also called as lower quartile, middle quartile (or median), and upper quartile respectively.

Let us now see about the concept of each quartile one by one.

First Quartile (Q1) separates the first one-fourth (1/4th) part of the given data from the rest of the upper three-fourth (3/4th) part i.e. first 25% of the data will lie below Q1 and the remaining 75% will lie above it, mathematical formula for Q1 is given below, where N is the total number of observations in the data set.

Second Quartile (Q2) divides the given data into two equal parts. It separates the first half of the given data from its second half i.e. 50% of the data lie under Q2 and the remaining 50% lie above it. The second quartile (Q2) is also called the median of the data.

The third Quartile (Q3) separates the first three quarters (3/4th) of the given data from the last quarter i.e. 75% of the given data will lie below Q3 and 25% will lie above it.

Points to remember

• The first quartile (Q1) is considered as the median of the first half of the given data set      

• The third quartile (Q3) is considered as the median of the second half of the given data set

• The second quartile (Q2) of a distribution is equal to the median if the given data

Example:

 Calculate all the three quartiles for the given data set.

First, we have to sort the given data in ascending order as given below;

From now total observation count is N = 12. Now we will calculate the three quartiles using the formulas

Q1 = 1 * (12+1)/4 = 13/4 = 3.25

= 3rd observation + 0.25*(4th observation – 3rd observation)

= 48 + 0.25(51 – 48) = 48.75

Q2 = 2 * (12+1)/4 = 26/4 = 6.5

= 6th observation + 0.5*(7th observation – 6th observation)

= 60 + 0.5(62 – 60) = 61

Q3 = 3 * (12+1)/4 = 39/4 = 9.75

= 9th observation + 0.75*(10th observation – 9th observation)

= 66 + 0.75(70 – 66) = 69

Deciles:

Deciles are the partition values which divides the given data set into ten equal parts. There are nine deciles denoted as D1, D2, D3,…, and D9 and they are called the 1st Decile, 2nd Decile, 3rd Decile,…., 9th Decile respectively. For decile calculation, the given data should be sorted in either ascending or descending order.

• The 1st Decile (D1) is the point that has 10% of the observations under it and the remaining 90% observations above it

• The 2nd Decile (D2) is the point that has 20% of the observations below it and the remaining 80% observations above it

• Similarly, the 9th Decile (D9) is the point that has 90% of the observations below it and the remaining 10% observations above it

• The 5th decile (D5) is the same as median because it divides the given data into two equal parts.

Mathematical representation of the ith decile

Percentiles-

Percentiles divides a given data into 100 equal parts, it divides the complete data set into hundred groups of 1% each. There are total of 99 percentiles denoted as P1, P2, P3,…, and, P99, and they are known as 1st percentile, 2nd percentile,…., 99th percentile respectively. Here it is crucial that the data should be sorted in either ascending or descending order of magnitude before percentile calculation.

The kth percentile is that value in a data set that splits the data into two parts:

• The lower part contains k percent of the given data

• The upper part contains the rest of the given data which amounts to (100 – k) percent, where k is any number between 0 and 100.

The 50th percentile is equal to the median of the given data which divides the series into two equal parts, and the 25th, 50th & 75th percentiles are also called the first quartile (Q1), second quartile (Q2), third quartile (Q3) respectively. Hence Mathematically the formula for ith  percentile (Pi) is represented as;

Conclusion:

To summarize, we have covered all the three partition values in this article in other words all the types of data, these concepts have a variety of applications in our day-to-day data life. We have also solved examples based on the concepts which helped us to understand the partition values.