Presentation of Data.pptx

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Presentation of DataModule 6

Basic Statistics



Presentation of Data

Objectives: At the end of the lesson, thestudents should be able to:

1. Prepare a stemandleaf plot

!. "escribe data in te#tual form

$. %onstruct fre&uenc' distribution table

(. %reate )raphs*. +ead and interpret )raphs and tables



Ungrouped vs. Grouped Data

"ata can be classified as )rouped orun)rouped.

Ungrouped data are data that arenot or)anied, or if arran)ed, could

onl' be from hi)hest to lo-est orlo-est to hi)hest.

Grouped data are data that are

or)anied and arran)ed intodifferent classes or cate)ories.



Presentation of Data

e#tual

Method• +earran)ement

from lo-est tohi)hest

• Stemandleaf

plot

abular

Method• /re&uenc'

distributiontable 0/"

• +elative /"• %umulative /"• %ontin)enc'

able

2raphical

Method• Bar %hart• 3isto)ram• /re&uenc'

Pol')on• Pie %hart• 4ess than,

)reater thanO)ive





Textual Presentation of Data

#ample. 7ou are as8ed to present theperformance of 'our section in the

Statistics test. he follo-in) are the testscores of 'our class:

$( (! !9 *9 1 ; $( ($

*9 1< $* ($ *9 !$ !$ $*

$ $< $< $; $; $< $< $;

!( !; !* !6 !< ! (( ((

(; (< (6 (* (* (6 (* (6



/irst, arran)e the data in order for 'ou to

identif' the important characteristics. his can

be done in t-o -a's: rearran)in) from lo-estto hi)hest or usin) the stemandleaf plot.

Belo- is the rearran)ement of data from

lo-est to hi)hest:

; !$ !< $* $< ($ (* (<

1 !( !; $ $; ($ (* (;

1< !* $( $< $; (( (6 *9

!9 !6 $( $< $; (( (6 *9

!$ ! $* $< (! (* (6 *9



=ith the rearran)ed data, pertinent

data -orth mentionin) can be easil'

reco)nied. he follo-in) is one -a' ofpresentin) data in te#tual form.

In the Statistics class of 40students, 3 obtained the perfect scoreof 50. Sixteen students got a score of40 and above, while only 3 got 1 and

below. !enerally, the studentsperfor"ed well in the test with #3 or$0% getting a passing score of 3& andabove.



Another way of rearranging data is by

making use of the stem-and-leaf plot.

Stem-and-leaf Plot is a table -hich sortsdata accordin) to a certain pattern. 5t

involves separatin) a number into t-o parts.5n a t-odi)it number, the stem consists ofthe first di)it, and the leaf consists of thesecond di)it. =hile in a threedi)it number,

the stem consists of the first t-o di)its, andthe leaf consists of the last di)it. 5n a onedi)it number, the stem is ero.

'hat is a ste"(and(leafplot)



Belo- is the stemandleaf plot of theun)rouped data )iven in the e#ample.

Stem 4eaves

9 ;

1 ,<

! 9,$,$,(,*,6,,<,;

$ (,(,*,*,,<,<,<,<,;,;,;

( !,$,$,(,(,*,*,*,6,6,6,<,;

* 9,9,9

>tiliin) the stemandleaf plot, -e can readil' see the order ofthe data. hus, -e can sa' that the top ten )ot scores *9, *9,*9, (;, (<, (6, (6, (6,(*, and (* and the ten lo-est scores are;, 1, 1<, !9, !$,!$,!(,!*,!6, and !.



Tabular Presentation of Data http:??---.s-s.or).ph?'outh.htm

able @umber

able itle

%olumn 3eader

+o- %lassifier

Bod'

Source @ote

Belo- is a sample of a table -ith all of its partsindicated:



Frequency Distribution Table

A fre&uenc' distribution table is a table-hich sho-s the data arran)ed into

different classes0or cate)ories and thenumber of cases0or fre&uencies -hich fallinto each class.

he follo-in) is an illustration of afre&uenc' distribution table for un)roupeddata:



Sample of a Frequency DistributionTable for Ungrouped Data

Table 1.1

/re&uenc' "istribution for the A)es of *9 Studentsnrolled in Statistics

Age Frequency

1! !

1$ 1$

1( !

1* (

16 $

1 1

@ *9



Sample of a Frequency Distribution

Table for Grouped Data

able 1.!

/re&uenc' "istribution able for the ui Scores of

*9 Students in 2eometr'

0 - 2 1

3 - 5 2

6 - 8 13

9 - 11 15

12 - 14 19

Scores Frequency



are the smallest numbers that can actuall' belon)

to different classes

0 - 2 1

3 - 5 2

6 - 8 13

9 - 11 15

12 - 14 19

Rating Frequency

o!er "lass imits



Lower Class

Liits

0 - 2 1

3 - 5 2

6 - 8 13

9 - 11 15

12 - 14 19

Rating Frequency

are the smallest numbers that can actuall' belon)

to different classes

o!er "lass imits



0 - 2 1

3 - 5 2

6 - 8 13

9 - 11 15

12 - 14 19

Rating Frequency

are the lar)est numbers that can actuall' belon) to

different classes

Upper "lass imits



!""er Class

Liits

0 - 2 1

3 - 5 2

6 - 8 13

9 - 11 15

12 - 14 19

Rating Frequency

are the lar)est numbers that can actuall' belon) to

different classes

Upper "lass imits



are the numbers used to separate classes, but

-ithout the )aps created b' class limits

"lass #oundaries



0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Rating Frequency

- 0#5

2#5

5#5

8#5

11#5

14#5

number separatin) classes

"lass #oundaries



Class

$oun%aries

0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Rating Frequency

- 0#5

2#5

5#5

8#5

11#5

14#5

number separatin) classes

"lass #oundaries



he %lass Mar8 or %lass Midpoint is the respective

avera)e of each class limits

"lass $idpoints



Class

&i%"oints

0 - 1 2 20

3 - 4 5 14

6 - ' 8 15

9 - 10 11 2

12 - 13 14 1

Rating Frequency

midpoints of the classes

"lass $idpoints



0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Rating Frequency

is the difference bet-een t-o consecutive lo-er

class limits or t-o consecutive class boundaries

"lass %idt&



Class

(i%t)

3 0 - 2 20

3 3 - 5 14

3 6 - 8 15

3 9 - 11 2

3 12 - 14 1

Rating Frequency

is the difference bet-een t-o consecutive lo-er

class limits or t-o consecutive class boundaries

"lass %idt&



1. Be sure that the classes are mutuall' e#clusive.

!. 5nclude all classes, even if the fre&uenc' is ero.

$. r' to use the same -idth for all classes.

(. Select convenient numbers for class limits.

*. >se bet-een * and !9 classes.

6. he sum of the class fre&uencies must e&ual thenumber of ori)inal data values.

*ui%elines +or Frequency ,ales



3. Select for the first lower limit either the lowest score or a convenient value slightlyless than the lowest score.

4. Add the class width to the starting point to get the second lower class limit, add the

width to the second lower limit to get the third, and so on.

5. List the lower class limits in a vertical column and enter the upper class limits.

6. Represent each score y a tally mar! in the appropriate class.

"otal tally mar!s to find the total fre#uency for each class.

Constructing . Frequency ,ale$. %ecide on the numer of classes .

&. %etermine the class width y dividing the range y the numer of classes'range ( highest score ) lowest score* and round up.

class wi%t) roun% up o+

range

nuer o+ classes



relati/e +requency class +requency

su o+ all +requencies

Relati/e Frequency ,ale



0 - 2 20

3 - 5 14

6 - 8 15

9 - 11 2

12 - 14 1

Rating Frequency

0 - 2 38#5

3 - 5 26#9

6 - 8 28#8

9 - 11 3#8

12 - 14 1#9

RatingRelati/e

Frequency

2052 38#5

1452 26#9

etc#

Table 2-5,otal +requency 52

Relati/e Frequency ,ale



Cuulati/e

Frequencies

0 - 2 20 20 52

3 5 14 34 32

6 8 15 49 18

9 11 2 51 3

12 14 1 52 1

Rating c+

Table 2-6

c+ Frequency

Cuulati/e Frequency ,ale



Table 2-6Table 2-5Table 2-3

Frequency ,ales



"omplete FDT

A complete /" has class mar8 or midpoint0#, class boundaries 0c.b, relative

fre&uenc' or percenta)e fre&uenc', and theless than cumulative fre&uenc' 0Ccf andthe )reater than cumulative fre&uenc'0Dcf.



Table 2-6

Grouped Frequency Distribution for t&e TestScores of '( Students in Statistics

Co"lete Frequency ,ales

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