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Quantiles

Reporters:GROUP 8

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Quantiles Is a score distribution where the scores are divided

into different equal parts.

There are three kinds of quantiles:

Quartileis a score point that divides the scoresin the distribution into four (4) equal parts.

Decileis a score point that divides the scores in

the distribution into ten (10) equal parts.

Percentileis a score point that divides the score

in the distribution hundred (100) equal parts.

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Quantiles for Ungrouped Dataa. Quartile for Ungrouped Data

=

4 + 1

4

=

1

4 + 1

1

4

=2

4 + 1

2

4

=3

4

+ 1 3

4

where,

is the indicated quartile

k = 1, 2, 3

n = number of cases

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b. Decile for Ungrouped Data

=

10 + 1

10

=1

10 + 1

1

10

=

2

10 + 1

2

10

=3

10 + 1

3

10

=9

10

+ 1 9

10

where,

is the indicated decile

k = 1, 2, 3, 4, 5, 6, 7, 8, 9

n = number of cases

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c. Percentile for Ungrouped Data

= 100

+ 1 100

=1

100 + 1

1

100

=2

100 + 1 2

100

=3

100 + 1

3

100

=25

100 + 1

25

100

=50

100 + 1

50

100

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=90

100

+ 1 90

100

=98

100 + 1

98

100

=99

100 + 1

99

100

where,

is the indicated percentile

k = 1, 2, 3, 4, 5,.97, 98, 99

n = number of cases

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Example:

Using the given data 6,8,10,12,12,14,15,16,20.Find , , , , , .

x(score)

6

8

10

12

12

1415

16

20

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1. Solve for .

n = 9 =

1

4 + 1

1

4

=1

4(9) + 1

1

4

=9

4+

3

4

=12

4

= 3

The value of is 10 which is the 3rd score in the

distribution. Therefore, 25% of the scores are below 10.

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3. Solve for .

=

6

10 (9) + 1

6

10

=54

10+

4

10

=

58

10

= 5.8

The value of lies in the sum of the 5thscore and 80%

of the difference between the 6thand 5thscores.

= 5th

score + 0.80(6th

score5th

score)= 12 + 0.80(14 - 12)

= 12 + 0.80 (2)

= 13.60

Therefore, 60% of the scores in the distribution are less

than 13.60.

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4. Solve for .

=9

10(9) + 1

9

10

=81

10+

1

10

=82

10

= 8.2

The value of lies within the 8thand 9thscores. That is, the

sum of 8thscore and 20% of the difference between the 9 thand 8thscores.

= 8thscore + 0.20(9thscore8thscore)

= 12 + 0.20(20 - 16)= 12 + 0.20 (4)

= 12 + .80

= 16.80

Therefore, 90% of the scores in the distribution are less than

16.80.

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5. Solve the value of .

=65

100 + 1

65

100

=65

100(9) + 1

65

100

=585

100 + 1 65

100

=585

100+

35

100

=

620

100

= 6.20

Therefore, lies within the 6thand 7thscores. The value of

is the sum of the 6thand 20% of the difference between

the 7thand the 6thscores.

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= 6thscore + 0.20(7thscore6thscore)

= 14 + 0.20(15 - 14)

= 14 + 0.20 (1)= 14 + .20

= 14.20

Therefore, 65% of the scores in the distribution are less

than 14.20.

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6. Solve the value of .

=99

100 + 1 99

100

=99

100(9) + 1

99

100

=

891

100 + 1

99

100

=891

100+

1

100

=892

100

= 8.92

Therefore, lies within the 8thand 9thscores. The value of

is the sum of the 8thand 92% of the difference between

the 9thand the 8thscores.

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= 8thscore + 0.92(9thscore8thscore)

= 16 + 0.92(20 - 16)

= 16 + 0.92 (4)= 16 + 3.68

= 19.68

Therefore, 99% of the scores in the distribution are less

than 19.68.

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Quantiles for Grouped Dataa. Quartiles for Grouped Data

The general formula for the quartile is = +

c.i,

where:

is the indicated quartilek = 1, 2, and 3

= lower boundary of the quartile class

= cumulative frequency before the quartile class whenscores are arranged from lowest to highest.

= frequency of quartile classc.i = size of the class interval

QC = is a class or category containing

for ,

for and

for

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= +

4

.

= +

24

.

= +

34

.

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Solution:

=

= 12.5

QC= 41 48LL = 41

LB = 40.5

cfp = 10

fq = 5

c.i = 8

Q = LB +

n4

cfp

fqc. i

Q = 40.5 +

12.5 10

5 8

Q = 40.5 +2.5

58

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Q = 40.5 +20

5

Q = 40.5 + 4

Q = 44.50

Therefore, 25% of the scores of 50 students who

participated in the test are less than 44.50.

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b. Deciles for Grouped Data

The general formula for the quartile is = +

c.i,

where:

is the indicated decile

k = 1, 2, 3, 4, 5, 6, 7, 8 , 9

= lower boundary of the indicated decile class= cumulative frequency before the quartile class when

scores are arranged from lowest to highest.

= frequency of the indicated decile class

c.i = size of the class interval

DC = is a class or category containing

for ,

for and

for ..

for

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Example 2: The data for the score of fifty(50) students in

Filipino class are given below. Solve for the value of .

X f cf