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Grouped Data Deciles

The document discusses percentiles and provides an example to calculate the 21st and 45th percentiles (P21 and P45) from a table of math scores of 50 students grouped into classes. It shows the steps to find the class boundaries and cumulative frequencies to determine the values corresponding to P21 and P45.

Uploaded by

Friah Mae Delgado
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229 views52 pages

Grouped Data Deciles

The document discusses percentiles and provides an example to calculate the 21st and 45th percentiles (P21 and P45) from a table of math scores of 50 students grouped into classes. It shows the steps to find the class boundaries and cumulative frequencies to determine the values corresponding to P21 and P45.

Uploaded by

Friah Mae Delgado
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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GROUPED DATA:

PERCENTILES
GROUPED DATA: PERCENTILES

• PERCENTILES
the score values that divides a distribution into 100 equal parts
GROUPED DATA: PERCENTILES

[ ]
𝑘𝑁
−𝑐𝑓 𝑏
10 0
𝑃 𝑘= 𝐿𝐵 +
= Lower Class Boundary
= nth percentile 𝑖
𝑓𝑃
= total frequency
= Cumulative Frequency of the class before the percentile
𝑘 class
= Frequency of the percentile class
= class width/class size (size of class interval)
GROUPED DATA: DECILES

𝑘𝑁
𝑃 𝑘 𝑐𝑙𝑎𝑠𝑠=
= nth percentile

100
= total frequency
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4
41 - 45 8
36 - 40 11
31 - 35 9
26 - 30 12
21 - 25 6
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4
41 - 45 8
36 - 40 11
31 - 35 9
26 - 30 12 Lower limit Upper limit
21 - 25 6
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4
41 - 45 8
36 - 40 11
31 - 35 9
26 - 30 12
21 - 25 6
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4
41 - 45 8
36 - 40 11
31 - 35 9
26 - 30 12
21 - 25 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8
36 - 40 11
31 - 35 9
26 - 30 12
21 - 25 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11
31 - 35 9
26 - 30 12
21 - 25 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11 35.5
31 - 35 9
26 - 30 12
21 - 25 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11 35.5
31 - 35 9 30.5
26 - 30 12
21 - 25 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11 35.5
31 - 35 9 30.5
26 - 30 12 25.5
21 - 25 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11 35.5
31 - 35 9 30.5
26 - 30 12 25.5
21 - 25 6 20.5

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11 35.5
31 - 35 9 30.5
26 - 30 12 25.5
21 - 25 6 20.5

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11 35.5
31 - 35 9 30.5
26 - 30 12 25.5
21 - 25 6 20.5 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11 35.5
31 - 35 9 30.5
26 - 30 12 25.5 18
21 - 25 6 20.5 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11 35.5
31 - 35 9 30.5 27
26 - 30 12 25.5 18
21 - 25 6 20.5 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5
36 - 40 11 35.5 38
31 - 35 9 30.5 27
26 - 30 12 25.5 18
21 - 25 6 20.5 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5
41 - 45 8 40.5 46
36 - 40 11 35.5 38
31 - 35 9 30.5 27
26 - 30 12 25.5 18
21 - 25 6 20.5 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
46 - 50 4 45.5 50
41 - 45 8 40.5 46
36 - 40 11 35.5 38
31 - 35 9 30.5 27
26 - 30 12 25.5 18
21 - 25 6 20.5 6

i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class
f LB < cf
Interval
46 - 50 4 45.5 50
41 - 45 8 40.5 46
36 - 40 11 35.5 38
31 - 35 9 30.5 27
26 - 30 12 25.5 18 10.5
21 - 25 6 20.5 6
i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class
f LB < cf
Interval
46 - 50 4 45.5 50
41 - 45 8 40.5 46
36 - 40 11 35.5 38
31 - 35 9 30.5 27
26 - 30 12 25.5 18
21 - 25 6 20.5 6
i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class
f LB < cf
Interval
46 - 50 4 45.5 50
41 - 45 8 40.5 46
36 - 40 11 35.5 38
31 - 35 9 30.5 27
26 - 30 12 25.5 18
21 - 25 6 20.5 6
i=5 n = 50
EXAMPLE

The table shows the Math-10 scores of 50 students. Calculate the


value of P21 and P45.
Class
f LB < cf
Interval
46 - 50 4 45.5 50
41 - 45 8 40.5 46
36 - 40 11 35.5 38
31 - 35 9 30.5 27
26 - 30 12 25.5 18
21 - 25 6 20.5 6
i=5 n = 50
EXAMPLE
EXAMPLE

No. of Class Intervals: Range: R = Highest Value – Lowest Value


2k > n R = 48 – 13
26 > 40 R = 35
64 > 40
k=6 Class Width:
i = R/k i = 35/6 i = 5.833, round off to 6
EXAMPLE

k=6 R = 35 i=6
EXAMPLE

Class
f
Interval

k=6 R = 35 i=6
EXAMPLE

Class
f
Interval
13
k=6 R = 35 i=6
EXAMPLE

Class
f
Interval
13
k=6 R = 35 i=6 19
EXAMPLE

Class
f
Interval
13
k=6 R = 35 i=6 19
25
31
37
43
EXAMPLE

Class
f
Interval
13 - 18
k=6 R = 35 i=6 19 - 24
25
31
37
43
EXAMPLE

Class
f
Interval
13 - 18
k=6 R = 35 i=6 19 - 24
25 - 30
31 - 36
37 - 42
43 - 48
EXAMPLE

Class
f
Interval
13 - 18 8
k=6 R = 35 i=6 19 - 24
25 - 30
31 - 36
37 - 42
43 - 48
EXAMPLE

Class
f
Interval
13 - 18 8
k=6 R = 35 i=6 19 - 24 10
25 - 30
31 - 36
37 - 42
43 - 48
EXAMPLE

Class
f
Interval
13 - 18 8
k=6 R = 35 i=6 19 - 24 10
25 - 30 12
31 - 36
37 - 42
43 - 48
EXAMPLE

Class
f
Interval
13 - 18 8
k=6 R = 35 i=6 19 - 24 10
25 - 30 12
31 - 36 4
37 - 42
43 - 48
EXAMPLE

Class
f
Interval
13 - 18 8
k=6 R = 35 i=6 19 - 24 10
25 - 30 12
31 - 36 4
37 - 42 3
43 - 48
EXAMPLE

Class
f
Interval
13 - 18 8
k=6 R = 35 i=6 19 - 24 10
25 - 30 12
31 - 36 4
37 - 42 3
43 - 48 3
i=6 n = 40
EXAMPLE

Class Interval f LB < cf

13 - 18 8
19 - 24 10
25 - 30 12
31 - 36 4
37 - 42 3
43 - 48 3

i=6 n = 40
EXAMPLE

Class Interval f LB < cf

13 - 18 8 12.5
19 - 24 10 18.5
25 - 30 12 24.5
31 - 36 4 30.5
37 - 42 3 36.5
43 - 48 3 42.5

i=6 n = 40
EXAMPLE

Class Interval f LB < cf

13 - 18 8 12.5 8
19 - 24 10 18.5 18
25 - 30 12 24.5 30
31 - 36 4 30.5 34
37 - 42 3 36.5 37
43 - 48 3 42.5 40

i=6 n = 40
GROUPED DATA:
PERCENTILE RANK
GROUPED DATA: PERCENTILE RANK

• PERCENTILE RANK
the percentile rank of a given score is the percentage of scores in its
frequency distribution that are less than that score.
GROUPED DATA: PERCENTILE RANK

100
𝑃 𝑃𝑅 = +
( 𝑃− 𝐿𝐵 ) 𝑓 𝑝
= Lower Class Boundary

𝑁 𝑖
= total frequency
+𝑐𝑓 [
= Frequency of the percentile class
= class width/class size (size of class interval)
= cumulative frequency
]
EXAMPLE

Calculate the percentile rank of 24 in the distribution.

Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
26 - 30 6
21 - 25 15
16 - 20 10
11 - 15 5
6 - 10 4
EXAMPLE

Calculate the percentile rank of 24 in the distribution.

Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
26 - 30 6
21 - 25 15
16 - 20 10
11 - 15 5
6 - 10 4

i=5 n = 40
EXAMPLE

Calculate the percentile rank of 24 in the distribution.

Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
26 - 30 6 25.5
21 - 25 15 20.5
16 - 20 10 15.5
11 - 15 5 10.5
6 - 10 4 5.5

i=5 n = 40
EXAMPLE

Calculate the percentile rank of 24 in the distribution.

Class Interval Frequency (f) Lower Boundary (LB) Less than Cumulative
Frequency (<cf)
26 - 30 6 25.5 40
21 - 25 15 20.5 34
16 - 20 10 15.5 19
11 - 15 5 10.5 9
6 - 10 4 5.5 4

i=5 n = 40
EXAMPLE

Calculate the percentile rank of 24 in the distribution.

Class
f LB < cf
Interval
26 - 30 6 25.5 40
21 - 25 15 20.5 34
16 - 20 10 15.5 19
11 - 15 5 10.5 9
6 - 10 4 5.5 4

i=5 n = 40
THANK YOU

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