Upper Quartile and the Method of Finding it for Raw Data

If the data are arranged in ascending or descending order then the variate lying at the middle between the largest and the median is called the upper quartile (or the third quartile), and it denoted by Q3.


In order to calculate the upper quartile of raw data, follow these steps.

Step I: Arrange the data in ascending order.

Step II: Finding the number of variates in the data. Let it be n. Then find the upper quartile as follows. If n is not divisible by 4 then the mth variate is the upper quartile, where m is the integer just greater than 3n4.

If n is divisible by 4 then the upper quartile is the mean of the 3n4th variate and the variate just greater then it.

Solved Problems on Upper Quartile and the Method of Finding it for Raw Data:

1. Find the upper quartile of the first thirteen natural numbers.

Solution:

The variates in ascending order are

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

Here n = 13.

So, 3n4 = 3×134 = 394 = 934

So, m = 10.

Therefore, the tenth variates is the upper quartile.

Hence, the upper quartile Q3 = 10.

 

2. If the variate 13 is removed from the above example, what will be the upper quartile?

Solution:

The variates in ascending order are

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Here, n = 12.

So, 3n4 = 3×124 = 364 = 9, i.e., 3n4 is an integer.

Therefore, the mean of the 9th and 10th variates is Q3 (the upper quartile).

Therefore, Q3 = 9+102 = 192 = 9.5.

Upper Quartile and the Method of Finding it for Raw Data

3. The following data represent the number of books issued by a library on 12 different days.

96, 180, 98, 75, 270, 80, 102, 100, 94, 75, 200, 610.

Find the upper quartile

Solution:

Write the data in ascending order, we have

75, 75, 80, 94, 96, 98, 100, 102, 180, 200, 270, 610.

Here, n = 12.

So, 3n4 = 3×124 = 364 = 9, i.e., 3n4 is an integer.

Therefore, the mean of the 9th and 10th variates is Q3 (the upper quartile).

Therefore, Q3 = 180+2002 = 3802 = 190.







9th Grade Math

From Upper Quartile and the Method of Finding it for Raw Data to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More