# 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 $$\frac{3n}{4}$$.

If n is divisible by 4 then the upper quartile is the mean of the $$\frac{3n}{4}$$th 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, $$\frac{3n}{4}$$ = $$\frac{3 × 13}{4}$$ = $$\frac{39}{4}$$ = 9$$\frac{3}{4}$$

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, $$\frac{3n}{4}$$ = $$\frac{3 × 12}{4}$$ = $$\frac{36}{4}$$ = 9, i.e., $$\frac{3n}{4}$$ is an integer.

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

Therefore, Q3 = $$\frac{9 + 10}{2}$$ = $$\frac{19}{2}$$ = 9.5.

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, $$\frac{3n}{4}$$ = $$\frac{3 × 12}{4}$$ = $$\frac{36}{4}$$ = 9, i.e., $$\frac{3n}{4}$$ is an integer.

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

Therefore, Q3 = $$\frac{180 + 200}{2}$$ = $$\frac{380}{2}$$ = 190.

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.

## Recent Articles

1. ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

Sep 15, 24 04:57 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…

2. ### Counting Before, After and Between Numbers up to 10 | Number Counting

Sep 15, 24 04:08 PM

Counting before, after and between numbers up to 10 improves the child’s counting skills.

3. ### Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 15, 24 03:16 PM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as:

4. ### 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 14, 24 04:31 PM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.