Find the Quartiles for Arrayed Data

Here we will learn how to find the quartiles for arrayed data.

Step I: Arrange the grouped data in ascending order and from a frequency table.

Step II: Prepare a cumulative-frequency table of the data.

Step III: (i) For Q1: Select the cumulative frequency that is just greater than \(\frac{N}{4}\), where N is the total number of observations. The variate whose cumulative frequency is the selected cumulative frequency, is Q1.

(ii) For Q3: Select the cumulative frequency that is just greater than \(\frac{3N}{4}\), where N is the total number of observations. The variate whose cumulative frequency is the selected cumulative frequency, is Q3.


Note: In case \(\frac{N}{4}\) or \(\frac{3N}{4}\) is equal to the cumulative frequency of the variate, take the mean of the variate and the next variate.


Solved Examples on Find the Quartiles for Arrayed Data:

1. Find the lower and upper quartiles of the following distribution.


Variate

2

4

6

8

10

Frequency

3

2

5

4

2


Solution:

The cumulative-frequency table of the data is as below.


Variate

2

4

6

8

10

Frequency

3

2

5

4

2


N = 16

Cumulative Frequency

3

5

10

14

16


Here, \(\frac{N}{4}\) = \(\frac{16}{4}\) = 4.

The cumulative frequency just greater than 4 is 5.

The variate whose cumulative frequency is 5 is 4.

So, Q1 = 4.

Next, \(\frac{3N}{4}\) = \(\frac{3 × 16}{4}\) = \(\frac{48}{4}\) = 12.

The cumulative frequency just greater than 12 is 14.

The variate whose cumulative frequency is 14 is 8.


Find the Quartiles for Arrayed Data

2. Marks obtained by 70 students in an examination are given below.

Find the upper quartile.


Marks

25

50

35

65

45

70

Number of Students

6

15

12

10

18

9


Solution:

Arrange the data in ascending order, the cumulative-frequency table is constructed as below.


Marks

25

35

45

50

65

70

Frequency

6

12

18

15

10

9

Cumulative Frequency

6

18

36

51

61

70


Here, \(\frac{N}{4}\) = \(\frac{70}{4}\) = \(\frac{35}{2}\) = 17.5.

Cumulative frequency just greater than 17.5 is 18.

The variate whose cumulative frequency is 18, is 35. 

So, Q1 = 35.


Again, \(\frac{3N}{4}\) = \(\frac{3 × 70}{4}\) = \(\frac{105}{4}\) = 52.5.

Cumulative frequency just greater than 52.5 is 61.

The variate whose cumulative frequency is 61, is 65.

Therefore, Q3 = 65.






9th Grade Math

From Find the Quartiles for Arrayed 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. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Jul 12, 24 03:08 PM

    Fractions
    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Worksheet on Fractions | Questions on Fractions | Representation | Ans

    Jul 12, 24 02:11 PM

    Worksheet on Fractions
    In worksheet on fractions, all grade students can practice the questions on fractions on a whole number and also on representation of a fraction. This exercise sheet on fractions can be practiced

    Read More

  3. Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

    Jul 12, 24 03:21 AM

    Fraction 8/16
    There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1…

    Read More

  4. Conversion of Improper Fractions into Mixed Fractions |Solved Examples

    Jul 12, 24 12:59 AM

    To convert an improper fraction into a mixed number, divide the numerator of the given improper fraction by its denominator. The quotient will represent the whole number and the remainder so obtained…

    Read More

  5. Conversion of Mixed Fractions into Improper Fractions |Solved Examples

    Jul 12, 24 12:30 AM

    Conversion of Mixed Fractions into Improper Fractions
    To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the proper fraction and then to the product add the numerator of the fraction to get the numerat…

    Read More