What are Quartiles?
Quartiles are used in descriptive statistics. It is used to describe one-fourth of the given data. Quartiles refer to the 3 points, which divide the whole data taken for statistics into four equal parts. Here is an overview about the three points or quartiles:
• The first quartile i.e. the first point will separate the first quarter of the data. It is also called as lower Quartile or 25th percentile.
• The second quartile is the median or the middle point, which divides the whole data into two halves. This can be termed as 50th percentile.
• The third quartile is the point that splits the highest quarter of the data from the data set. This is called as the upper quartile or the 75th percentile.
The data values till Q1 is the first quarter, the data values in between the points Q1 and Q2 is the second quarter, the data values in between the points Q2 and Q3 is the third quarter and the data values after Q3 is the fourth quarter. This is the way the three quartiles divide the whole data set into four quarters.
How to find Quartiles?
Now that you know what a quartile is, the next step is to know how to find quartiles. For finding quartiles, we have to know where the three points or the quartiles lie on the given data set. In order to find quartile, sort the values in the given data set in the ascending order.
The quartiles or the points can be found out by using the formula: L is equal to y multiplied by (x divided by 100). Here, x refers to the percentile for the first, second and third quartiles respectively and y refers to the number of data values present in the given data set in which the data values are arranged in ascending order. L refers to the location of the quartile.
Examples of Quartiles
Let us consider a class of 20 students whose English marks have to be compared to find the number of students who are below average, average and excellent in English subject.
The marks obtained by the students are 80, 73, 64, 99, 67, 96, 87, 53, 43, 97, 78, 90, 69, 81, 40, 35, 100, 96, 93, and 98.
The above data is arranged in ascending order as: 35, 40, 43, 53, 67, 64, 69, 73, 78, 80, 81, 87, 90, 93, 96, 96, 97, 98, 99, and 100.
As per formula the 25th percentile will be 20 multiplied by 25 divided by 100 which will be 5. As the value of L25 is 5, the number in the 5th location is the first quartile which is 67. By similar calculations we get the 50th percentile or L50 i.e. 80 as the second quartile which is the 10th position and the third quartile is 96 which is in the 15th position or L75 in the data set. Based on the three quartiles, the four quarters are identified as highlighted below in red:
35, 40, 43, 53, 67, 64, 69, 73, 78, 80, 81, 87, 90, 93, 96, 96, 97, 98, 99, 100
Students within 67 marks are below average. Students who scored from 67 to 96 are average scorers and students scoring above 96 to 100 are excellent performers.
Know more about the statistics tutor. This article gives basic information about finding quartiles . Next article will try to cover more statistics help topics and its problems and many more. Please share your comments.
Quartiles are used in descriptive statistics. It is used to describe one-fourth of the given data. Quartiles refer to the 3 points, which divide the whole data taken for statistics into four equal parts. Here is an overview about the three points or quartiles:
• The first quartile i.e. the first point will separate the first quarter of the data. It is also called as lower Quartile or 25th percentile.
• The second quartile is the median or the middle point, which divides the whole data into two halves. This can be termed as 50th percentile.
• The third quartile is the point that splits the highest quarter of the data from the data set. This is called as the upper quartile or the 75th percentile.
The data values till Q1 is the first quarter, the data values in between the points Q1 and Q2 is the second quarter, the data values in between the points Q2 and Q3 is the third quarter and the data values after Q3 is the fourth quarter. This is the way the three quartiles divide the whole data set into four quarters.
How to find Quartiles?
Now that you know what a quartile is, the next step is to know how to find quartiles. For finding quartiles, we have to know where the three points or the quartiles lie on the given data set. In order to find quartile, sort the values in the given data set in the ascending order.
The quartiles or the points can be found out by using the formula: L is equal to y multiplied by (x divided by 100). Here, x refers to the percentile for the first, second and third quartiles respectively and y refers to the number of data values present in the given data set in which the data values are arranged in ascending order. L refers to the location of the quartile.
Examples of Quartiles
Let us consider a class of 20 students whose English marks have to be compared to find the number of students who are below average, average and excellent in English subject.
The marks obtained by the students are 80, 73, 64, 99, 67, 96, 87, 53, 43, 97, 78, 90, 69, 81, 40, 35, 100, 96, 93, and 98.
The above data is arranged in ascending order as: 35, 40, 43, 53, 67, 64, 69, 73, 78, 80, 81, 87, 90, 93, 96, 96, 97, 98, 99, and 100.
As per formula the 25th percentile will be 20 multiplied by 25 divided by 100 which will be 5. As the value of L25 is 5, the number in the 5th location is the first quartile which is 67. By similar calculations we get the 50th percentile or L50 i.e. 80 as the second quartile which is the 10th position and the third quartile is 96 which is in the 15th position or L75 in the data set. Based on the three quartiles, the four quarters are identified as highlighted below in red:
35, 40, 43, 53, 67, 64, 69, 73, 78, 80, 81, 87, 90, 93, 96, 96, 97, 98, 99, 100
Students within 67 marks are below average. Students who scored from 67 to 96 are average scorers and students scoring above 96 to 100 are excellent performers.
Know more about the statistics tutor. This article gives basic information about finding quartiles . Next article will try to cover more statistics help topics and its problems and many more. Please share your comments.
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